What is the solution for (d^2y)/(dt^2)+3(dy)/(dt)-10y=0 ?

The solution for (d^2y)/(dt^2)+3(dy)/(dt)-10y=0 is y=c_{1}e^{2t}+c_{2}e^{-5t}

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(d^2y)/(dt^2)+3(dy)/(dt)-10y=0

\frac{d ^{2} y}{d t ^{2}} + 3 \frac{d y}{d t} - 10 y = 0

y = c_{1} e^{2 t} + c_{2} e^{- 5 t}

Solution steps

\frac{d ^{2} y}{d t ^{2}} + 3 \frac{d y}{d t} - 10 y = 0

Solve linear ODE:

y = c_{1} e^{2 t} + c_{2} e^{- 5 t}

y = c_{1} e^{2 t} + c_{2} e^{- 5 t}

y^{^{''}} + 10 y^{^{'}} + 34 y = 0, y (0) = 1, y^{^{'}} (0) = 2

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

x^{^{''}} - 26 x^{^{'}} + 25 x = 0, x (0) = - 1, x^{^{'}} (0) = 2

D^{2} (D + 4)^{3} y = 0

y^{^{'''}} - 8 y^{^{''}} + 15 y^{^{'}} = 0

What is the solution for (d^2y)/(dt^2)+3(dy)/(dt)-10y=0 ?
The solution for (d^2y)/(dt^2)+3(dy)/(dt)-10y=0 is y=c_{1}e^{2t}+c_{2}e^{-5t}