What is the solution for 5(d^2y)/(dx^2)-7(dy)/(dx)-90y=0 ?

The solution for 5(d^2y)/(dx^2)-7(dy)/(dx)-90y=0 is y=c_{1}e^{5x}+c_{2}e^{-(18x)/5}

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5(d^2y)/(dx^2)-7(dy)/(dx)-90y=0

5 \frac{d ^{2} y}{d x ^{2}} - 7 \frac{d y}{d x} - 90 y = 0

y = c_{1} e^{5 x} + c_{2} e^{- \frac{18 x}{5}}

Solution steps

5 \frac{d ^{2} y}{d x ^{2}} - 7 \frac{d y}{d x} - 90 y = 0

Solve linear ODE:

y = c_{1} e^{5 x} + c_{2} e^{- \frac{18 x}{5}}

y = c_{1} e^{5 x} + c_{2} e^{- \frac{18 x}{5}}

y^{^{''}} - 9 y = 0, y^{^{'}} (0) = 0

y^{^{''}} - 25 y = 0, y (0) = 1, y^{^{'}} (0) = 0

\frac{d ^{2} y}{d x ^{2}} - 7 \frac{d y}{d x} = 0

(\frac{1}{9} d^{2} - 8 d - 2) y = 0

y^{^{''}} - 25 y = 0, y (0) = 0, y^{^{'}} (0) = 20

What is the solution for 5(d^2y)/(dx^2)-7(dy)/(dx)-90y=0 ?
The solution for 5(d^2y)/(dx^2)-7(dy)/(dx)-90y=0 is y=c_{1}e^{5x}+c_{2}e^{-(18x)/5}