What is the solution for (d^2)/(dx^2)xy+2x^2=5 ?

The solution for (d^2)/(dx^2)xy+2x^2=5 is y=(5x)/2-(x^3)/6+c_{1}+(c_{2})/x

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(d^2)/(dx^2)xy+2x^2=5

\frac{d ^{2}}{d x ^{2}} x y + 2 x^{2} = 5

y = \frac{5 x}{2} - \frac{x ^{3}}{6} + c_{1} + \frac{c _{2}}{x}

Solution steps

\frac{d ^{2}}{d x ^{2}} (x y) + 2 x^{2} = 5

Isolate

(x y)^{''} : (x y)^{''} = 5 - 2 x^{2}

Solve

(x y)^{''} = 5 - 2 x^{2} : (x y)^{'} = 5 x - \frac{2 x ^{3}}{3} + c_{1}

Solve

(x y)^{'} = 5 x - \frac{2 x ^{3}}{3} + c_{1} : y = \frac{5 x}{2} - \frac{x ^{3}}{6} + c_{1} + \frac{c _{2}}{x}

y = \frac{5 x}{2} - \frac{x ^{3}}{6} + c_{1} + \frac{c _{2}}{x}

\int sin^{3} (x) \cdot cos (x) d x

\frac{7}{x + 4}

\int x^{3} e^{x^{4} + 5} d x

y + y^{4} = (y^{6} + 3 x) y^{^{'}}

What is the solution for (d^2)/(dx^2)xy+2x^2=5 ?
The solution for (d^2)/(dx^2)xy+2x^2=5 is y=(5x)/2-(x^3)/6+c_{1}+(c_{2})/x