What is the solution for (d^2y)/(dx^2)-12(dy)/(dx)+35y=0 ?

The solution for (d^2y)/(dx^2)-12(dy)/(dx)+35y=0 is y=c_{1}e^{7x}+c_{2}e^{5x}

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(d^2y)/(dx^2)-12(dy)/(dx)+35y=0

\frac{d ^{2} y}{d x ^{2}} - 12 \frac{d y}{d x} + 35 y = 0

y = c_{1} e^{7 x} + c_{2} e^{5 x}

Solution steps

\frac{d ^{2} y}{d x ^{2}} - 12 \frac{d y}{d x} + 35 y = 0

Solve linear ODE:

y = c_{1} e^{7 x} + c_{2} e^{5 x}

y = c_{1} e^{7 x} + c_{2} e^{5 x}

y^{^{''}} + y^{^{'}} + 3.25 y = 0

y^{^{''}} - (2 a - 1) y^{^{'}} + a (a - 1) y = 0

16 y^{^{''}} + 9 y = 0

33 y^{^{''''}} + 323 y^{^{''}} + 400 y = 0

\frac{d ^{2} y}{d t ^{2}} - 4 \frac{d y}{d t} + 4 y = 0

What is the solution for (d^2y)/(dx^2)-12(dy)/(dx)+35y=0 ?
The solution for (d^2y)/(dx^2)-12(dy)/(dx)+35y=0 is y=c_{1}e^{7x}+c_{2}e^{5x}