What is the solution for (dy)/(dx)=e^{2x}-3y,y(0)=1 ?

The solution for (dy)/(dx)=e^{2x}-3y,y(0)=1 is y=(e^{2x})/5+4/(5e^{3x)}

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(dy)/(dx)=e^{2x}-3y,y(0)=1

\frac{d y}{d x} = e^{2 x} - 3 y, y (0) = 1

y = \frac{e ^{2 x}}{5} + \frac{4}{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{4}{5 e ^{3 x}}

y = \frac{e ^{2 x}}{5} + \frac{4}{5 e ^{3 x}}

4 sec (x) - 8 cos (x)

\int_{0}^{1} x e^{- 7 x^{2}} d x

\int \frac{e ^{c o s^{2} (x)}}{csc ( 2 x )} d x

\int \frac{e ^{- x}}{x ^{2}} d x

\int sec^{2} (1) d x

What is the solution for (dy)/(dx)=e^{2x}-3y,y(0)=1 ?
The solution for (dy)/(dx)=e^{2x}-3y,y(0)=1 is y=(e^{2x})/5+4/(5e^{3x)}