What is the solution for 4(dx)/(dt)+8x=16e^{-3t},x(0)=10 ?

The solution for 4(dx)/(dt)+8x=16e^{-3t},x(0)=10 is x=-4/(e^{3t)}+(14)/(e^{2t)}

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4(dx)/(dt)+8x=16e^{-3t},x(0)=10

4 \frac{d x}{d t} + 8 x = 16 e^{- 3 t}, x (0) = 10

x = - \frac{4}{e ^{3 t}} + \frac{14}{e ^{2 t}}

Solution steps

4 \frac{d x}{d t} + 8 x = 16 e^{- 3 t}

Solve linear ODE:

x = - \frac{4}{e ^{3 t}} + \frac{14}{e ^{2 t}}

x = - \frac{4}{e ^{3 t}} + \frac{14}{e ^{2 t}}

\int - \frac{1}{( x + 2 ) ^{2}} d x

x y^{^{'}} = 4 y

\int \frac{1}{49 e ^{- 4 x} + e ^{4 x}} d x

ln (1 + 4 x), 0

\frac{25}{s ^{2} + 6 s + 25}

What is the solution for 4(dx)/(dt)+8x=16e^{-3t},x(0)=10 ?
The solution for 4(dx)/(dt)+8x=16e^{-3t},x(0)=10 is x=-4/(e^{3t)}+(14)/(e^{2t)}