Paper 2, Section I, B

Differential Equations | Part IA, 2015

Find the general solution of the equation

dydx2y=eλx\frac{d y}{d x}-2 y=e^{\lambda x}

where λ\lambda is a constant not equal to 2 .

By subtracting from the particular integral an appropriate multiple of the complementary function, obtain the limit as λ2\lambda \rightarrow 2 of the general solution of ()(*) and confirm that it yields the general solution for λ=2\lambda=2.

Solve equation ()(*) with λ=2\lambda=2 and y(1)=2y(1)=2.

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