What is the solution for (dy)/(dx)=e^{2x}-3y,y(0)=2 ?

The solution for (dy)/(dx)=e^{2x}-3y,y(0)=2 is y=(e^{2x})/5+9/(5e^{3x)}

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(dy)/(dx)=e^{2x}-3y,y(0)=2

\frac{d y}{d x} = e^{2 x} - 3 y, y (0) = 2

y = \frac{e ^{2 x}}{5} + \frac{9}{5 e ^{3 x}}

Solution steps

\frac{d y}{d x} = e^{2 x} - 3 y

Solve linear ODE:

y = \frac{e ^{2 x}}{5} + \frac{9}{5 e ^{3 x}}

y = \frac{e ^{2 x}}{5} + \frac{9}{5 e ^{3 x}}

What is the solution for (dy)/(dx)=e^{2x}-3y,y(0)=2 ?
The solution for (dy)/(dx)=e^{2x}-3y,y(0)=2 is y=(e^{2x})/5+9/(5e^{3x)}