What is the solution for x(dy)/(dx)=y+(x^2-2)^2 ?

The solution for x(dy)/(dx)=y+(x^2-2)^2 is y=-x^4-4x^2+c_{1}x+(4x^4)/3-4

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x(dy)/(dx)=y+(x^2-2)^2

x \frac{d y}{d x} = y + (x^{2} - 2)^{2}

y = - x^{4} - 4 x^{2} + c_{1} x + \frac{4 x ^{4}}{3} - 4

Solution steps

x \frac{d y}{d x} = y + (x^{2} - 2)^{2}

Solve linear ODE:

y = - x^{4} - 4 x^{2} + c_{1} x + \frac{4 x ^{4}}{3} - 4

y = - x^{4} - 4 x^{2} + c_{1} x + \frac{4 x ^{4}}{3} - 4

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\frac{d}{d x} (csc^{2} (1 - 2 x))

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What is the solution for x(dy)/(dx)=y+(x^2-2)^2 ?
The solution for x(dy)/(dx)=y+(x^2-2)^2 is y=-x^4-4x^2+c_{1}x+(4x^4)/3-4