What is the solution for x(dy)/(dx)+2y=10x^2 ?

The solution for x(dy)/(dx)+2y=10x^2 is y=(5x^2)/2+(c_{1})/(x^2)

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x(dy)/(dx)+2y=10x^2

x \frac{d y}{d x} + 2 y = 10 x^{2}

y = \frac{5 x ^{2}}{2} + \frac{c _{1}}{x ^{2}}

Solution steps

x \frac{d y}{d x} + 2 y = 10 x^{2}

Solve linear ODE:

y = \frac{5 x ^{2}}{2} + \frac{c _{1}}{x ^{2}}

y = \frac{5 x ^{2}}{2} + \frac{c _{1}}{x ^{2}}

\int (1 + x^{2})^{2} d x

\int \frac{3 - 6 x ^{3} + 4 x ^{6}}{x ^{6}} d x

f (x) = \frac{( 6 ln ( x ) )}{x}

\int e^{(- x)} d x

\frac{d}{d x} (\frac{1}{2} x^{3})

What is the solution for x(dy)/(dx)+2y=10x^2 ?
The solution for x(dy)/(dx)+2y=10x^2 is y=(5x^2)/2+(c_{1})/(x^2)