What is the solution for y^'-5y=8,e^{5x}y(0)=0 ?

The solution for y^'-5y=8,e^{5x}y(0)=0 is y=(e^{5x+c_{1}})/5-8/5

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y^'-5y=8,e^{5x}y(0)=0

y^{^{'}} - 5 y = 8, e^{5 x} y (0) = 0

y = \frac{e ^{5 x + c_{1}}}{5} - \frac{8}{5}

Solution steps

y^{'} (x) - 5 y = 8

Solve separable ODE:

y = \frac{e ^{5 x + c_{1}}}{5} - \frac{8}{5}

y = \frac{e ^{5 x + c_{1}}}{5} - \frac{8}{5}

\frac{d x}{d t} = 2 x x

8 x \frac{d y}{d x} = - \frac{1}{y ^{3} 1 + x}

\frac{d y}{d t} + e^{t} y = 24 e^{t}

\frac{y d t}{d y} = t^{2} - 10 t + 21

What is the solution for y^'-5y=8,e^{5x}y(0)=0 ?
The solution for y^'-5y=8,e^{5x}y(0)=0 is y=(e^{5x+c_{1}})/5-8/5