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Popular >

y^{''}=ay^'

Solution

y^{^{''}} = a y^{^{'}}

Solution

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

Solution steps

y^{''} (t) = a y^{'} (t)

Solve linear ODE:

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

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

Graph

Popular Examples

y^{''}-10y^'+25y=0,y(0)=xe^{5x}

y^{^{''}} - 10 y^{^{'}} + 25 y = 0, y (0) = x e^{5 x}

9y^{''}-12y^'+4y=0,y(0)=2,y^'(0)=1

9 y^{^{''}} - 12 y^{^{'}} + 4 y = 0, y (0) = 2, y^{^{'}} (0) = 1

(d^2y)/(dx^2)-10(dy)/(dx)+29y=0

\frac{d ^{2} y}{d x ^{2}} - 10 \frac{d y}{d x} + 29 y = 0

y^{''}+10y^'+16y=0,y(0)=1,y^'(0)=0

y^{^{''}} + 10 y^{^{'}} + 16 y = 0, y (0) = 1, y^{^{'}} (0) = 0

y^{''}+ky^'+8y=0,y(0)=e^{2x}sin(2x)

y^{^{''}} + k y^{^{'}} + 8 y = 0, y (0) = e^{2 x} sin (2 x)

Frequently Asked Questions (FAQ)

What is the solution for y^{''}=ay^' ?
The solution for y^{''}=ay^' is y=c_{1}e^{at}+c_{2}