What is the solution for y^{''}-2/x y^'-(10)/(x^2)=0 ?

The solution for y^{''}-2/x y^'-(10)/(x^2)=0 is y=c_{1}x^3+c_{2}-10/9-10/3 ln(x)

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y^{''}-2/x y^'-(10)/(x^2)=0

y^{^{''}} - \frac{2}{x} y^{^{'}} - \frac{10}{x ^{2}} = 0

y = c_{1} x^{3} + c_{2} - \frac{10}{9} - \frac{10}{3} ln (x)

Solution steps

y^{''} (x) - \frac{2}{x} y^{'} (x) - \frac{10}{x ^{2}} = 0

Solve linear ODE:

y = c_{1} x^{3} + c_{2} - \frac{10}{9} - \frac{10}{3} ln (x)

y = c_{1} x^{3} + c_{2} - \frac{10}{9} - \frac{10}{3} ln (x)

What is the solution for y^{''}-2/x y^'-(10)/(x^2)=0 ?
The solution for y^{''}-2/x y^'-(10)/(x^2)=0 is y=c_{1}x^3+c_{2}-10/9-10/3 ln(x)