What is the solution for \H(x)(x)^2x^2dx-2x^3d\H(x)=0 ?

The solution for \H(x)(x)^2x^2dx-2x^3d\H(x)=0 is f(x)=e^{(x^2)/4+c_{1}}

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\H(x)(x)^2x^2dx-2x^3d\H(x)=0

H (x) (x)^{2} x^{2} d x - 2 x^{3} d H (x) = 0

f (x) = e^{\frac{x ^{2}}{4} + c_{1}}

Solution steps

H (x) x^{2} x^{2} d x - 2 x^{3} d H (x) = 0

Solve separable ODE:

f (x) = e^{\frac{x ^{2}}{4} + c_{1}}

f (x) = e^{\frac{x ^{2}}{4} + c_{1}}

y^{^{'}} = x (10 - y)

\frac{d y}{d x} = - \frac{5}{7} x^{3} y^{2}

y \frac{d y}{d x} + y^{3} = 1, y (4) = 0

(x^{2} + 25) y^{^{'}} = x y

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

What is the solution for \H(x)(x)^2x^2dx-2x^3d\H(x)=0 ?
The solution for \H(x)(x)^2x^2dx-2x^3d\H(x)=0 is f(x)=e^{(x^2)/4+c_{1}}