What is the solution for (d^2y)/(dx^2)-12(dy)/(dx)+36y=0 ?

The solution for (d^2y)/(dx^2)-12(dy)/(dx)+36y=0 is y=c_{1}e^{6x}+c_{2}xe^{6x}

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(d^2y)/(dx^2)-12(dy)/(dx)+36y=0

\frac{d ^{2} y}{d x ^{2}} - 12 \frac{d y}{d x} + 36 y = 0

y = c_{1} e^{6 x} + c_{2} x e^{6 x}

Solution steps

\frac{d ^{2} y}{d x ^{2}} - 12 \frac{d y}{d x} + 36 y = 0

Solve linear ODE:

y = c_{1} e^{6 x} + c_{2} x e^{6 x}

y = c_{1} e^{6 x} + c_{2} x e^{6 x}

\int_{0}^{42} 2 - x^{\frac{2}{5}} d x

\int tan (\frac{t}{2}) d t

\int_{0}^{1} (x + 7) (x - 8) d x

x \to - 4 lim (- x^{2} + 2 x - 8)

5 (e^{x})^{- 4}

What is the solution for (d^2y)/(dx^2)-12(dy)/(dx)+36y=0 ?
The solution for (d^2y)/(dx^2)-12(dy)/(dx)+36y=0 is y=c_{1}e^{6x}+c_{2}xe^{6x}