What is the solution for x^2(d^2y)/(dx^2)-5x(dy)/(dx)+9y=0 ?

The solution for x^2(d^2y)/(dx^2)-5x(dy)/(dx)+9y=0 is y=c_{1}x^3+c_{2}ln(x)x^3

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x^2(d^2y)/(dx^2)-5x(dy)/(dx)+9y=0

x^{2} \frac{d ^{2} y}{d x ^{2}} - 5 x \frac{d y}{d x} + 9 y = 0

y = c_{1} x^{3} + c_{2} ln (x) x^{3}

Solution steps

x^{2} \frac{d ^{2} y}{d x ^{2}} - 5 x \frac{d y}{d x} + 9 y = 0

Solve linear ODE:

y = c_{1} x^{3} + c_{2} ln (x) x^{3}

y = c_{1} x^{3} + c_{2} ln (x) x^{3}

\int \frac{( x ^{2} - x + 30 )}{x ^{3} + 5 x} d x

3 x + 6 x^{3}

\frac{d}{d x} (2^{x + 1})

\int e^{x} e^{2 x} + 4 d x

\int cos^{4} (x) \cdot sin^{3} (x) d x

What is the solution for x^2(d^2y)/(dx^2)-5x(dy)/(dx)+9y=0 ?
The solution for x^2(d^2y)/(dx^2)-5x(dy)/(dx)+9y=0 is y=c_{1}x^3+c_{2}ln(x)x^3