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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

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