Solve: dy/dx + y = e-x

1.	Solve: dy/dx + y = e-x
Answer» Given that dy/dx + 2y = e^-x This is a linear differential equation. Here P = 2; Q = e ∫P dx = ∫2 dx = 2x Thus, I.F = e∫Pdx = e^2x Hence the solution of (1) is ye^{∫ Pdx}= Qe^{∫ Pdx}dx + c That is, ye^2x = ∫e^-x e^2x dx + c (or) ye^2x = e^x + c (or) y = e^-x + ce^-2x is the required solution.

Answer»

Given that dy/dx + 2y = e^-x

This is a linear differential equation.

Here P = 2; Q = e

∫P dx = ∫2 dx = 2x

Thus, I.F = e∫Pdx = e^2x

Hence the solution of (1) is ye^{∫ Pdx}= Qe^{∫ Pdx}dx + c

That is, ye^2x = ∫e^-x e^2x dx + c (or) ye^2x = e^x + c (or) y = e^-x + ce^-2x is the required solution.

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Solve: dy/dx + y = e-x

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