# How do I solve this differential Equation

## Homework Statement

y3(dy/dx) = (y4 + 1)cosx

2. The attempt at a solution

I solved for the homogeneous equation which is y = Ce-sinx Where C is some constant

for the particular solution I tried Asinx + Bcosx where A and B are constants but when subbing in it's gets very messy.

How should I do this?

Thank you

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Chestermiller
Mentor
This looks like a variables separable problem.

Chet

Try some algebra to separate the variables and then integrate both sides.

LCKurtz
Homework Helper
Gold Member

## Homework Statement

y3(dy/dx) = (y4 + 1)cosx

2. The attempt at a solution

I solved for the homogeneous equation which is y = Ce-sinx Where C is some constant

for the particular solution I tried Asinx + Bcosx where A and B are constants but when subbing in it's gets very messy.

How should I do this?
You shouldn't. That method is for a linear (usually constant coefficient) DE.

Thanks for the replies, it was just a simple separation of variables problem. It's strange how you sometimes forget the basics as your knowledge grows.