What Is the Correct Method to Solve This Differential Equation?

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SUMMARY

The discussion centers on solving the differential equation y³(dy/dx) = (y⁴ + 1)cos(x). The user initially attempted to find a particular solution using the method of undetermined coefficients with Asin(x) + Bcos(x), but faced complications. The correct approach is to recognize this as a separable variables problem, allowing for straightforward integration after separating the variables. The user acknowledged the oversight of reverting to basic methods amidst advanced studies.

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  • Familiarity with the method of undetermined coefficients
  • Knowledge of integrating functions involving trigonometric identities
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Students and educators in mathematics, particularly those studying differential equations, as well as anyone looking to refresh their understanding of basic solution methods in this field.

baouba
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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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This looks like a variables separable problem.

Chet
 
Try some algebra to separate the variables and then integrate both sides.
 
baouba said:

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.
 

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