Solve differential equation y'+3x^2y= \sin(x)e^{-x^3}, \ y(0)=1

Joni Kenny

Joni Kenny

Answered question

2021-02-21

Solve differential equationy+3x2y=sin(x)ex3, y(0)=1

Answer & Explanation

au4gsf

au4gsf

Skilled2021-02-22Added 95 answers

y+p(x)y=q(x), p(x)=3x2, q(x)=sin(x)ex3
epdx=e3x2dx
epdx=e3x33
epdx=ex3
That is the I.F. is μ(x)=ex3
Multiply the integrating factor on both sides of the given equation
ex3y=sin(x)ex3ex3
ex3y=sin(x)[ex3ex3=ex3+x3=1]
Integrate both sides of the above equation
ddx(ex3y)dx=sin(x)dx
ex3y=cos(x)+c
y=cos(x)+cex3
Now compute the value of constant C by applying the given condition as follows
y(0)=cos(0)+ce(0)3
1=(1)+c1 [cos(0)=1]
1=1+c
1+1=c
2=c
Now substitute the value of C for the value of y and simplify further
y=cos(x)+2ex3

Do you have a similar question?

Recalculate according to your conditions!

New Questions in Differential Equations

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?