What is the solution for (dy)/(dx)-2e^{3x}-20e^{2x}=e^{3x} ?

The solution for (dy)/(dx)-2e^{3x}-20e^{2x}=e^{3x} is y=e^{3x}+10e^{2x}+c_{1}

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(dy)/(dx)-2e^{3x}-20e^{2x}=e^{3x}

\frac{d y}{d x} - 2 e^{3 x} - 20 e^{2 x} = e^{3 x}

y = e^{3 x} + 10 e^{2 x} + c_{1}

Solution steps

\frac{d y}{d x} - 2 e^{3 x} - 20 e^{2 x} = e^{3 x}

Substitute

\frac{d y}{d x}

with

y^{'} (x)

y^{^{'}} (x) - 2 e^{3 x} - 20 e^{2 x} = e^{3 x}

Isolate

y^{'} (x) : y^{'} (x) = 3 e^{3 x} + 20 e^{2 x}

f^{^{'}} (x) = g (x)

then

f (x) = \int g (x) d x

y = \int 3 e^{3 x} + 20 e^{2 x} d x

\int 3 e^{3 x} + 20 e^{2 x} d x = e^{3 x} + 10 e^{2 x} + c_{1}

y = e^{3 x} + 10 e^{2 x} + c_{1}

What is the solution for (dy)/(dx)-2e^{3x}-20e^{2x}=e^{3x} ?
The solution for (dy)/(dx)-2e^{3x}-20e^{2x}=e^{3x} is y=e^{3x}+10e^{2x}+c_{1}