What is the solution for y^'+3y=1-6e^{-2x} ?

The solution for y^'+3y=1-6e^{-2x} is y= 1/3-6/(e^{2x)}+(c_{1})/(e^{3x)}

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y^'+3y=1-6e^{-2x}

y^{^{'}} + 3 y = 1 - 6 e^{- 2 x}

y = \frac{1}{3} - \frac{6}{e ^{2 x}} + \frac{c _{1}}{e ^{3 x}}

Solution steps

y^{'} (x) + 3 y = 1 - 6 e^{- 2 x}

Solve linear ODE:

y = \frac{1}{3} - \frac{6}{e ^{2 x}} + \frac{c _{1}}{e ^{3 x}}

y = \frac{1}{3} - \frac{6}{e ^{2 x}} + \frac{c _{1}}{e ^{3 x}}

\int x^{2} \cdot 6^{x^{3}} d x

x \to - 9 + lim (\frac{∣ x + 9 ∣}{x + 9})

\int \frac{2 x}{x + 1} d x

h \to 0 lim (\frac{( 1 + h ) ^{6} - 1}{h})

\int (- 6 x^{2} + 4 x - 4 x cos (x)) d x

What is the solution for y^'+3y=1-6e^{-2x} ?
The solution for y^'+3y=1-6e^{-2x} is y= 1/3-6/(e^{2x)}+(c_{1})/(e^{3x)}