What is the solution for 4yx(dx)/(dy)=x^2+1 ?

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

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4yx(dx)/(dy)=x^2+1

4 y x \frac{d x}{d y} = x^{2} + 1

y = e^{c_{1}} x^{4} + 2 e^{c_{1}} x^{2} + e^{c_{1}}

Solution steps

4 y x \frac{d}{d y} (x) = x^{2} + 1

Solve separable ODE:

y = e^{c_{1}} x^{4} + 2 e^{c_{1}} x^{2} + e^{c_{1}}

y = e^{c_{1}} x^{4} + 2 e^{c_{1}} x^{2} + e^{c_{1}}

(x^{2} - 3) y^{^{'}} = x (y^{2} + 16), y (2) = 4

\frac{d y}{d x} = 3 y^{2} - y^{2} sin (x)

\frac{d y}{d x} = 3 x e^{3 x + y}

y e^{2 x} - (1 + e^{2 x}) \frac{d y}{d x} = 0

\frac{d y}{d x} + y cos (x) = 8 cos (x)

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