What Is the Correct Method to Solve This Differential Equation?

[baouba]

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

 

[Chestermiller]

This looks like a variables separable problem.

Chet

 

[paisiello2]

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

 

[LCKurtz]

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.

 

[baouba]

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.