What is the solution for x^2(d^2y)/(dx^2)+4x(dy)/(dx)+2y=8x ?

The solution for x^2(d^2y)/(dx^2)+4x(dy)/(dx)+2y=8x is y=(c_{1})/x+(c_{2}}{x^2}+\frac{4x)/3

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x^2(d^2y)/(dx^2)+4x(dy)/(dx)+2y=8x

x^{2} \frac{d ^{2} y}{d x ^{2}} + 4 x \frac{d y}{d x} + 2 y = 8 x

y = \frac{c _{1}}{x} + \frac{c _{2}}{x ^{2}} + \frac{4 x}{3}

Solution steps

x^{2} \frac{d ^{2} y}{d x ^{2}} + 4 x \frac{d y}{d x} + 2 y = 8 x

Solve linear ODE:

y = \frac{c _{1}}{x} + \frac{c _{2}}{x ^{2}} + \frac{4 x}{3}

y = \frac{c _{1}}{x} + \frac{c _{2}}{x ^{2}} + \frac{4 x}{3}

y = x^{2} - 8

\int_{- \infty}^{1} x e^{2 x} d x

\int x^{2} - a^{2} d x

- \frac{1}{4 s}

f (x) = x^{π^{2}} + (π^{2})^{x}

What is the solution for x^2(d^2y)/(dx^2)+4x(dy)/(dx)+2y=8x ?
The solution for x^2(d^2y)/(dx^2)+4x(dy)/(dx)+2y=8x is y=(c_{1})/x+(c_{2}}{x^2}+\frac{4x)/3