What is the solution for xsin(x^2)y^'+y(4x^2cos(x^2)-sin(x^2))=0 ?

The solution for xsin(x^2)y^'+y(4x^2cos(x^2)-sin(x^2))=0 is y=(c_{1}x)/(sin^2(x^2))

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xsin(x^2)y^'+y(4x^2cos(x^2)-sin(x^2))=0

x sin (x^{2}) y^{^{'}} + y (4 x^{2} cos (x^{2}) - sin (x^{2})) = 0

y = \frac{c _{1} x}{sin ^{2} ( x ^{2} )}

Solution steps

x sin (x^{2}) y^{'} (x) + y (4 x^{2} cos (x^{2}) - sin (x^{2})) = 0

Solve separable ODE:

y = \frac{c _{1} x}{sin ^{2} ( x ^{2} )}

y = \frac{c _{1} x}{sin ^{2} ( x ^{2} )}

What is the solution for xsin(x^2)y^'+y(4x^2cos(x^2)-sin(x^2))=0 ?
The solution for xsin(x^2)y^'+y(4x^2cos(x^2)-sin(x^2))=0 is y=(c_{1}x)/(sin^2(x^2))