The solution of the differential equation ( x + 1 ) d x d y − y = e 3 x ( x + 1 ) 2 is

The given equation is d x d y − x + 1 y = e 3 x ( x + 1 ) I.F. = e ∫ − x + 1 1 d x = e − l o g ( x + 1 ) = x + 1 1 The solution is y ( x + 1 1 ) = ∫ e 3 x ( x + 1 ) ⋅ x + 1 1 d x + a ⇒ x + 1 y = ∫ e 3 x d x + a = 3 e 3 x + a ⇒ x + 1 3 y = e 3 x + c , c = 3 a

Mathematics - Differential Equation Question with Solution | TestHub

MathematicsDifferential EquationLinear DE / Red. LDEEasy2 minPYQ_2020

MathematicsEasysingle choice

The solution of the differential equation $(x + 1) \frac{d y}{d x} - y = e^{3 x} (x + 1)^{2}$ is

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The given equation is $\frac{d y}{d x} - \frac{y}{x + 1} = e^{3 x} (x + 1)$ I.F. $= e^{\int - \frac{1}{x + 1} d x} = e^{- l o g (x + 1)} = \frac{1}{x + 1}$ The solution is $y (\frac{1}{x + 1}) = \int e^{3 x} (x + 1) \cdot \frac{1}{x + 1} d x + a$ $\Rightarrow \frac{y}{x + 1} = \int e^{3 x} d x + a = \frac{e ^{3 x}}{3} + a$ $\Rightarrow \frac{3 y}{x + 1} = e^{3 x} + c, c = 3 a$

Stream:BITSATSubject:MathematicsTopic:Differential EquationSubtopic:Linear DE / Red. LDE

⏱ 2mℹ️ Source: PYQ_2020

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