What is the solution for (d^2y)/(dx^2)(1)-(dy)/(dx)(10)+25y=0 ?

The solution for (d^2y)/(dx^2)(1)-(dy)/(dx)(10)+25y=0 is y=c_{1}e^{5x}+c_{2}xe^{5x}

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(d^2y)/(dx^2)(1)-(dy)/(dx)(10)+25y=0

\frac{d ^{2} y}{d x ^{2}} (1) - \frac{d y}{d x} (10) + 25 y = 0

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

Solution steps

\frac{d ^{2} y}{d x ^{2}} (1) - \frac{d y}{d x} (10) + 25 y = 0

Solve linear ODE:

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

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

y^{^{''}} + 64 y = 0, y (0) = 0, y^{^{'}} (0) = 8

0.5 \frac{d ^{2} y}{d x ^{2}} + 2 y = 0

12 y^{^{''}} - 12 y^{^{'}} + 150 y = 0

y^{^{''}} + 4 y^{^{'}} + 5 y = 0, y (0) = 2, y^{^{'}} (0) = 3

y^{^{''}} - 4 y^{^{'}} - 5 y = 0, y (0) = 2, y^{^{'}} (0) = 28

What is the solution for (d^2y)/(dx^2)(1)-(dy)/(dx)(10)+25y=0 ?
The solution for (d^2y)/(dx^2)(1)-(dy)/(dx)(10)+25y=0 is y=c_{1}e^{5x}+c_{2}xe^{5x}