What is the solution for 3x^2y^'+x^3y^{''}=x ?

The solution for 3x^2y^'+x^3y^{''}=x is y=c_{1}+(c_{2})/(x^2)+1/2 ln(x)-1/4

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3x^2y^'+x^3y^{''}=x

3 x^{2} y^{^{'}} + x^{3} y^{^{''}} = x

y = c_{1} + \frac{c _{2}}{x ^{2}} + \frac{1}{2} ln (x) - \frac{1}{4}

Solution steps

3 x^{2} y^{'} (x) + x^{3} y^{''} (x) = x

Solve linear ODE:

y = c_{1} + \frac{c _{2}}{x ^{2}} + \frac{1}{2} ln (x) - \frac{1}{4}

y = c_{1} + \frac{c _{2}}{x ^{2}} + \frac{1}{2} ln (x) - \frac{1}{4}

\int \frac{x ^{2} - 3}{- x ^{3} + 9 x + 1} d x

\int (2 x - 3) (5 x + 1) d x

\int_{1}^{5} \frac{4}{x} d x

n = 1 \sum \infty \frac{2}{3 ^{n} + 1}

\frac{d}{d x} (cot (tan (x)))

What is the solution for 3x^2y^'+x^3y^{''}=x ?
The solution for 3x^2y^'+x^3y^{''}=x is y=c_{1}+(c_{2})/(x^2)+1/2 ln(x)-1/4