What is the solution for (d^2y)/(dt^2)-4(dy)/(dt)=0 ?

The solution for (d^2y)/(dt^2)-4(dy)/(dt)=0 is y=c_{1}e^{4t}+c_{2}

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(d^2y)/(dt^2)-4(dy)/(dt)=0

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

y = c_{1} e^{4 t} + c_{2}

Solution steps

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

Solve linear ODE:

y = c_{1} e^{4 t} + c_{2}

y = c_{1} e^{4 t} + c_{2}

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

\frac{d ^{2} f}{d x ^{2}} = f (x)

(0 + 1) y^{^{''}} + (7 + 1) y^{^{'}} - (6 + 1) y = 0

4 y^{^{''}} + y^{^{'}} - 3 y = 0

y^{^{''}} - 2 y - 3 y^{^{'}} = 0

What is the solution for (d^2y)/(dt^2)-4(dy)/(dt)=0 ?
The solution for (d^2y)/(dt^2)-4(dy)/(dt)=0 is y=c_{1}e^{4t}+c_{2}