What is the solution for (dv)/(dt)=0.32v+0.22(100e^{0.32t}) ?

The solution for (dv)/(dt)=0.32v+0.22(100e^{0.32t}) is v=22e^{0.32t}t+c_{1}e^{0.32t}

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(dv)/(dt)=0.32v+0.22(100e^{0.32t})

\frac{d v}{d t} = 0.32 v + 0.22 (100 e^{0.32 t})

v = 22 e^{0.32 t} t + c_{1} e^{0.32 t}

Solution steps

\frac{d v}{d t} = 0.32 v + 0.22 (100 e^{0.32 t})

Solve linear ODE:

v = 22 e^{0.32 t} t + c_{1} e^{0.32 t}

v = 22 e^{0.32 t} t + c_{1} e^{0.32 t}

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\int \frac{x}{( x - 6 ) ( x + 2 ) ^{2}} d x

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\int x + 1 d x

\frac{d}{d y} (\frac{y}{( x ^{2} + y ^{2} + z ^{2} ) ^{\frac{3}{2}}})

What is the solution for (dv)/(dt)=0.32v+0.22(100e^{0.32t}) ?
The solution for (dv)/(dt)=0.32v+0.22(100e^{0.32t}) is v=22e^{0.32t}t+c_{1}e^{0.32t}