What is the solution for (d^2y)/(dx^2)(x^2)-9x(dy)/(dx)+(61y)=0 ?

The solution for (d^2y)/(dx^2)(x^2)-9x(dy)/(dx)+(61y)=0 is y=x^5(c_{1}cos(6ln(x))+c_{2}sin(6ln(x)))

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(d^2y)/(dx^2)(x^2)-9x(dy)/(dx)+(61y)=0

\frac{d ^{2} y}{d x ^{2}} (x^{2}) - 9 x \frac{d y}{d x} + (61 y) = 0

y = x^{5} (c_{1} cos (6 ln (x)) + c_{2} sin (6 ln (x)))

Solution steps

\frac{d ^{2} y}{d x ^{2}} (x^{2}) - 9 x \frac{d y}{d x} + (61 y) = 0

Solve linear ODE:

y = x^{5} (c_{1} cos (6 ln (x)) + c_{2} sin (6 ln (x)))

y = x^{5} (c_{1} cos (6 ln (x)) + c_{2} sin (6 ln (x)))

x \to - 1 lim (2 x^{2} + 3 x - 5)

(f (6 x))^{2} + 3

(6, 0), (4, 6)

\frac{d}{d y} (y^{\frac{3}{2}})

\int \frac{1}{x 9 - x} d x

What is the solution for (d^2y)/(dx^2)(x^2)-9x(dy)/(dx)+(61y)=0 ?
The solution for (d^2y)/(dx^2)(x^2)-9x(dy)/(dx)+(61y)=0 is y=x^5(c_{1}cos(6ln(x))+c_{2}sin(6ln(x)))