Question 1

Find the general solution: ${ }^{9 y^{\prime \prime \prime}-12 y^{\prime \prime}-11 y^{\prime}-2 y=0}$

Accepted Answer

The answer of Find the general solution: \({ }^{9 y^{\prime...

Question 2

Find the general solution: $y^{\prime}=\frac{3 y x^{2}}{x^{3}+1}$

Accepted Answer

The answer of Find the general solution: $y^{\prime}=\frac{3 y x^{2}}{x^{3}+1}$...

Question 3

Find the general solution: $y^{\prime \prime}-10 y^{\prime}+34 y=0$

Accepted Answer

The answer of Find the general solution: \(y^{\prime \prime}-10 y^{\prime}+34...

Question 4

Find the general solution: $e^{-x} y^{\prime}-y e^{-x}=1$

Accepted Answer

The answer of Find the general solution: $e^{-x} y^{\prime}-y e^{-x}=1$...

Question 5

Find the particular solution: $y^{\prime \prime}+8 y^{\prime}+20 y=0, y^{\prime}=2$ at $(0,3)$

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The answer of Find the particular solution: \(y^{\prime \prime}+8 y^{\prime}+20...

Question 6

Find the orthogonal trajectories of the family of curves $x=k y^{2}$, where $k$ is a constant.

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Question 7

Solve the differential equation: $y^{\prime \prime}+16 y=\sin 4 x$, when $y^{\prime}(0,1)=8$

Accepted Answer

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Question 8

Is the function $y=2 C x^{2}$ a solution to the differential equation $y^{\prime \prime}+2 y^{\prime}+2 y=\frac{2 y(1+x)^{2}}{x^{2}}$ ?

Accepted Answer

A) True 
 B)False

Question 9

Solve: $y^{\prime \prime}-6 y^{\prime}+9 y=x^{2}+1$

Accepted Answer

The answer of Solve: $y^{\prime \prime}-6 y^{\prime}+9 y=x^{2}+1$...

Question 10

Find the equation of the curve that passes through $(1,0)$ whose slope is $y' = \frac{y+1}{x}$

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The answer of Find the equation of the curve that...

Question 11

Find the general solution: $\left(x-3 x^{3}\right) y^{\prime}-3 x^{2} y-y=0$

Accepted Answer

The answer of Find the general solution: \(\left(x-3 x^{3}\right) y^{\prime}-3...

Question 12

Solve the differential equation: $y^{\prime \prime}+2 y^{\prime}=4 e^{x}-5$

Accepted Answer

The answer of Solve the differential equation: \(y^{\prime \prime}+2 y^{\prime}=4...

Question 13

Find the particular solution of the differential equation: $y^{\prime}=(1-y) \cos x$, when $y(\pi)=2$

Accepted Answer

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Question 14

Find the general solution: $\left(x^{2}+y^{2}\right) d x=x y d y$

Accepted Answer

The answer of Find the general solution: \(\left(x^{2}+y^{2}\right) d x=x...

Question 15

Find the general solution: $e^{x} y y^{\prime}=1$

Accepted Answer

The answer of Find the general solution: $e^{x} y y^{\prime}=1$...

Question 16

Find the general solution: $2 x d y=2 y d x+5 x^{2} d y$

Accepted Answer

The answer of Find the general solution: \(2 x d...

Question 17

Solve the differential equation: $y^{\prime \prime}+2 y^{\prime}+y=e^{-x}$

Accepted Answer

The answer of Solve the differential equation: $y^{\prime \prime}+2 y^{\prime}+y=e^{-x}$...

Question 18

Find the particular solution: $\left(y^{2}-x y\right) d x+\left(3 x^{2}-x y\right) d y=0 ; x=1$ and $y=3$

Accepted Answer

The answer of Find the particular solution: \(\left(y^{2}-x y\right) d...

Question 19

Solve: $y^{\prime \prime}+y^{\prime}-6 y=7 x$

Accepted Answer

The answer of Solve: $y^{\prime \prime}+y^{\prime}-6 y=7 x$...

Question 20

Find the general solution: $y d y=x^{2} d x$

Accepted Answer

The answer of Find the general solution: \(y d y=x^{2}...

Exam 35: Differential Equations

Find the general solution: e−xy′−ye−x=1e^{-x} y^{\prime}-y e^{-x}=1e−xy′−ye−x=1

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Find the general solution: (x−3x3)y′−3x2y−y=0\left(x-3 x^{3}\right) y^{\prime}-3 x^{2} y-y=0(x−3x3)y′−3x2y−y=0

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Is the function y=2Cx2y=2 C x^{2}y=2Cx2 a solution to the differential equation y′′+2y′+2y=2y(1+x)2x2y^{\prime \prime}+2 y^{\prime}+2 y=\frac{2 y(1+x)^{2}}{x^{2}}y′′+2y′+2y=x22y(1+x)2​ ?

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Find the general solution: y′′−10y′+34y=0y^{\prime \prime}-10 y^{\prime}+34 y=0y′′−10y′+34y=0

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Find the general solution: 9y′′′−12y′′−11y′−2y=0{ }^{9 y^{\prime \prime \prime}-12 y^{\prime \prime}-11 y^{\prime}-2 y=0}9y′′′−12y′′−11y′−2y=0

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Find the particular solution: (y2−xy)dx+(3x2−xy)dy=0;x=1\left(y^{2}-x y\right) d x+\left(3 x^{2}-x y\right) d y=0 ; x=1(y2−xy)dx+(3x2−xy)dy=0;x=1 and y=3y=3y=3

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Find the particular solution of the differential equation: y′=(1−y)cos⁡xy^{\prime}=(1-y) \cos xy′=(1−y)cosx , when y(π)=2y(\pi)=2y(π)=2

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Solve the differential equation: y′′+2y′=4ex−5y^{\prime \prime}+2 y^{\prime}=4 e^{x}-5y′′+2y′=4ex−5

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Find the orthogonal trajectories of the family of curves x=ky2x=k y^{2}x=ky2 , where kkk is a constant.

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Solve the differential equation: y′′+2y′+y=e−xy^{\prime \prime}+2 y^{\prime}+y=e^{-x}y′′+2y′+y=e−x

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Find the particular solution: y′′+8y′+20y=0,y′=2y^{\prime \prime}+8 y^{\prime}+20 y=0, y^{\prime}=2y′′+8y′+20y=0,y′=2 at (0,3)(0,3)(0,3)

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Solve: y′′−6y′+9y=x2+1y^{\prime \prime}-6 y^{\prime}+9 y=x^{2}+1y′′−6y′+9y=x2+1

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Find the general solution: y′=3yx2x3+1y^{\prime}=\frac{3 y x^{2}}{x^{3}+1}y′=x3+13yx2​

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Find the equation of the curve that passes through (1,0)(1,0)(1,0) whose slope is y′=y+1xy' = \frac{y+1}{x}y′=xy+1​

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Find the general solution: ydy=x2dxy d y=x^{2} d xydy=x2dx

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Find the general solution: exyy′=1e^{x} y y^{\prime}=1exyy′=1

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Find the general solution: (x2+y2)dx=xydy\left(x^{2}+y^{2}\right) d x=x y d y(x2+y2)dx=xydy

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Find the general solution: 2xdy=2ydx+5x2dy2 x d y=2 y d x+5 x^{2} d y2xdy=2ydx+5x2dy

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Solve: y′′+y′−6y=7xy^{\prime \prime}+y^{\prime}-6 y=7 xy′′+y′−6y=7x

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Solve the differential equation: y′′+16y=sin⁡4xy^{\prime \prime}+16 y=\sin 4 xy′′+16y=sin4x , when y′(0,1)=8y^{\prime}(0,1)=8y′(0,1)=8

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Find the general solution: $e^{-x} y^{\prime}-y e^{-x}=1$

Correct Answer
verified

Find the general solution: $\left(x-3 x^{3}\right) y^{\prime}-3 x^{2} y-y=0$

Correct Answer
verified

Is the function $y=2 C x^{2}$ a solution to the differential equation $y^{\prime \prime}+2 y^{\prime}+2 y=\frac{2 y(1+x)^{2}}{x^{2}}$ ?

Correct Answer
verified

Find the general solution: $y^{\prime \prime}-10 y^{\prime}+34 y=0$

Correct Answer
verified

Find the general solution: ${ }^{9 y^{\prime \prime \prime}-12 y^{\prime \prime}-11 y^{\prime}-2 y=0}$

Correct Answer
verified

Find the particular solution: $\left(y^{2}-x y\right) d x+\left(3 x^{2}-x y\right) d y=0 ; x=1$ and $y=3$

Correct Answer
verified

Find the particular solution of the differential equation: $y^{\prime}=(1-y) \cos x$ , when $y(\pi)=2$

Correct Answer
verified

Solve the differential equation: $y^{\prime \prime}+2 y^{\prime}=4 e^{x}-5$

Correct Answer
verified

Find the orthogonal trajectories of the family of curves $x=k y^{2}$ , where $k$ is a constant.

Correct Answer
verified

Solve the differential equation: $y^{\prime \prime}+2 y^{\prime}+y=e^{-x}$

Correct Answer
verified

Find the particular solution: $y^{\prime \prime}+8 y^{\prime}+20 y=0, y^{\prime}=2$ at $(0,3)$

Correct Answer
verified

Solve: $y^{\prime \prime}-6 y^{\prime}+9 y=x^{2}+1$

Correct Answer
verified

Find the general solution: $y^{\prime}=\frac{3 y x^{2}}{x^{3}+1}$

Correct Answer
verified

Find the equation of the curve that passes through $(1,0)$ whose slope is $y' = \frac{y+1}{x}$

Correct Answer
verified

Find the general solution: $y d y=x^{2} d x$

Correct Answer
verified

Find the general solution: $e^{x} y y^{\prime}=1$

Correct Answer
verified

Find the general solution: $\left(x^{2}+y^{2}\right) d x=x y d y$

Correct Answer
verified

Find the general solution: $2 x d y=2 y d x+5 x^{2} d y$

Correct Answer
verified

Solve: $y^{\prime \prime}+y^{\prime}-6 y=7 x$

Correct Answer
verified

Solve the differential equation: $y^{\prime \prime}+16 y=\sin 4 x$ , when $y^{\prime}(0,1)=8$

Correct Answer
verified