Differential Eqns: particular soln to xy' + 4y = 15xcox(x^5)

[doggy]

I'm having a bit of trouble figuring out this differential equation. The question is:

Find the particular solution of the differential equation:
xy ' +4y = 15xcos(x^5) sastisfying the initial condition y(pi)=0.

[Martingale]

I'm having a bit of trouble figuring out this differential equation. The question is Find the particular solution of the differential equation:
xy ' +4y = 15xcos(x^5) sastisfying the initial condition y(pi)=0.

Use an Integrating factor.

[doggy]

I have tried using an integrating factor of x^4 but I'm still not getting the correct answer

[Martingale]

I have tried using an integrating factor of x^4 but I'm still not getting the correct answer

then

so

now take care of the initial condition

[doggy]

I have gotten up to that point as well but I'm having trouble with the conditions when I sub in pi I got:
3 cos(pi)^5/(pi)^4 + c/(pi/4) =0
thus c= -3 cos((pi)^5)

So the final answer should be :
3 cos (x^5) - 3 cos(pi)^5 but that's not correct

[Martingale]

I have gotten up to that point as well but I'm having trouble with the conditions when I sub in pi I got:
3 cos(pi)^5/(pi)^4 + c/(pi/4) =0
thus c= -3 cos((pi)^5)

So the final answer should be :
3 cos (x^5) - 3 cos(pi)^5 but that's not correct

Why do you have ?

[doggy]

Don't I need the cos (pi)^5?

[Martingale]

Don't I need the cos (pi)^5?

no.

so

now take care of the initial condition

solve for

[doggy]

So then the final answer would be c=0

and y= 3 sin(x^5)/x^4?

[Martingale]

So then the final answer would be c=0

and y= 3 sin(x^5)/x^4?

no