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(x+1)dy/dx - y = (e^3x(x+1) in linear differential equation |
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Answer» (x + 1) \(\frac{dy}{dx} - y\) = e3x (x + 1) \(\Rightarrow\) \(\frac{dy}{dx} - \frac{y}{x + 1} = e^{3x}\) ∴ \(P = \frac{-1}{x + 1},\) Q = e3x I.F. \(= e^{\int\,p\,dx} = e^{\int\,\frac{-1}{x + 1}}dx\) \(= e^{- \log (x + 1)}\) \(= e^{\log \left(\frac{1}{x + 1}\right)} = \frac{1}{x + 1}\) ∴ y × I.F. \(= \int Q \times (I.F.)dx\) \(\Rightarrow\) \(\frac{y}{x + 1} = \int \frac{e^{3x}}{x + 1}dx\) which is complete solution of given linear differential equation. |
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