What is a general solution to the differential equation \frac{dy}{dx}=\frac{x^{3}}{y^{2}}?

Kennedy Ford

Kennedy Ford

Answered question

2022-04-19

What is a general solution to the differential equation dydx=x3y2?

Answer & Explanation

fonne0kgq

fonne0kgq

Beginner2022-04-20Added 11 answers

Treat  dy  dx  like a fraction to move the y terms to one side of the equation and the x terms to the other:
 dy  dx =x3y2y2 dy =x3 dx 
Integrate both sides:
y2 dy =x3 dx 
Using the typical integration power rule:
y33=x44+C
Solving for y:
y3=3x44+C
y=3x44+C3

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