Maharashtra State BoardHSC Commerce 12th Board Exam
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Solve the following differential equation. dydx+y=e-x - Mathematics and Statistics

Sum

Solve the following differential equation.

`dy/dx + y = e ^-x`

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Solution

`dy/dx + y = e ^-x`

The given equation is of the form

`dy/dx + py = Q`

where, P = 1 and Q = e-x

∴ I.F. = `e int ^(pdx) = e int ^(1.dx)= e^x`

∴  Solution of the given equation is

`y (I.F.) = int Q (I.F.) dx + c`

∴  `y e^x = int e^-x e ^xdx+c`

∴  `y e^x = int 1dx +c`

∴  y ex = x+c

Concept: Differential Equations
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APPEARS IN

Balbharati Mathematics and Statistics 1 (Commerce) 12th Standard HSC Maharashtra State Board
Chapter 8 Differential Equation and Applications
Exercise 8.5 | Q 1.1 | Page 168
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