What is the solution for (d^2y)/(dx^2)=a(dy)/(dx) ?

The solution for (d^2y)/(dx^2)=a(dy)/(dx) is y=c_{1}e^{ax}+c_{2}

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(d^2y)/(dx^2)=a(dy)/(dx)

\frac{d ^{2} y}{d x ^{2}} = a \frac{d y}{d x}

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

Solution steps

\frac{d ^{2} y}{d x ^{2}} = a \frac{d y}{d x}

Solve linear ODE:

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

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

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

u^{^{''}} + a H (t) = 0

y^{^{''}} + 2 y^{^{'}} + 37 y = 0, y (0) = 2, y^{^{'}} (0) = - 26

y^{^{''}} + 2 y^{^{'}} + 100 y = 0, y (0) = 2, y (2) = 0

y^{^{''}} - 4 y^{^{'}} + 29 y = 0, y (0) = 4, y^{^{'}} (0) = 18

What is the solution for (d^2y)/(dx^2)=a(dy)/(dx) ?
The solution for (d^2y)/(dx^2)=a(dy)/(dx) is y=c_{1}e^{ax}+c_{2}