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  • Solve for General Solution. dy/dx + 3x = e^-2x

Solve for general solution:

    Q2.    \frac{dy}{dx} + 3y = e^{-2x}

Answers (1)

best_answer

Given equation is
\frac{dy}{dx} + 3y = e^{-2x}
This is  \frac{dy}{dx} + py = Q  type where p = 3 and Q = e^{-2x}
Now,
I.F. = e^{\int pdx}= e^{\int 3dx}= e^{3x}
Now, the solution of given differential equation is given by the relation
Y(I.F.) =\int (Q\times I.F.)dx +C
Y(e^{ 3x }) =\int (e^{-2x}\times e^{ 3x })dx +C
Y(e^{ 3x }) =\int (e^{x})dx +C\\ Y(e^{3x})= e^x+C\\ Y = e^{-2x}+Ce^{-3x}
Therefore, the general solution is Y = e^{-2x}+Ce^{-3x}

Posted by

Gautam harsolia

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