Question

Find the general solution of the following equation.y '(x) + 2y = -4

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asked 2021-05-18

Find the general solution of the following equation.
\(y '(x) + 2y = -4\)

Answers (1)

2021-05-19

Step 1
Given
\(y '(x) + 2y = -4\)
Calculation:
Step 2
\(y'+2y=-4\)
\(\frac{dy}{dx}+2y=-4\)
\(I.F.=e^{\int 2dx}\)
\(I.F.=e^{2x}\)
\(y\times I.F.=\int -4\times I.F.\)
\(y\times e^{2x}=\int -4\times e^{2x}dx\)
\(ye^{2x}=-4\int e^{2x}dx\)
\(ye^{2x}=-4\times \frac{e^{2x}}{2}+C\)
\(ye^{2x}=-2e^{2x}+C\)
\(y=-2+Ce^{-2x}\)

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