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Home  >>  CBSE XII  >>  Math  >>  Differential Equations
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Find the general solution of the differential equation$\large\frac{dy}{dx}$$+3y=e^{-2x}$

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Toolbox:
  • To solve the first order linear differential equation of the form $\large\frac{dy}{dx}$$ + Py = Q$
  • (i) Write the given equation in the form of $\large\frac{dy}{dx}$$ + Py = Q$
  • (ii) Find the integrating factor (I.F) = $e^{\int Pdx}$.
  • (iii) Write the solution as y(I.F) = integration of $Q(I.F) dx + C$
Step 1:
The given equation is a first order linear differnetial equation.
Using the information from the tool box to solve the equation, first let us find the I.F
$\int 3dx = 3x$, so the I.F is $e^3x$
Step 2:
$y.e^3x = \int e^{-2x}.e^{3x}.dx + C$
$y.e^{3x} =\int e^{(3x-2x)}dx + C$
$y.e^{3x} = \int e^xdx +c$
$y.e^{3x }= e^x + C$
Dividing throughout by $e^{3x}$
$y = e^{-2x} + Ce^{3x}$.
This is the required solution.
answered Aug 1, 2013 by sreemathi.v
 

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