What is the solution for x(dy)/(dx)+3y=(1+x)/(x^3) ?

The solution for x(dy)/(dx)+3y=(1+x)/(x^3) is y=(ln(x))/(x^3)+1/(x^2)+(c_{1})/(x^3)

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x(dy)/(dx)+3y=(1+x)/(x^3)

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

y = \frac{ln ( x )}{x ^{3}} + \frac{1}{x ^{2}} + \frac{c _{1}}{x ^{3}}

Solution steps

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

Solve linear ODE:

y = \frac{ln ( x )}{x ^{3}} + \frac{1}{x ^{2}} + \frac{c _{1}}{x ^{3}}

y = \frac{ln ( x )}{x ^{3}} + \frac{1}{x ^{2}} + \frac{c _{1}}{x ^{3}}

\int \frac{8}{1 - cos ( 4 x )} d x

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f (t) = 5 cos (8 t) + 3 e^{- 4} sin (3 t)

x \to 0 lim (ln (x) - x)

What is the solution for x(dy)/(dx)+3y=(1+x)/(x^3) ?
The solution for x(dy)/(dx)+3y=(1+x)/(x^3) is y=(ln(x))/(x^3)+1/(x^2)+(c_{1})/(x^3)