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Find the general solution of the differential equation$\large\frac{dy}{dx}+\frac{y}{x}$$=x^2$

1 Answer

  • 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:
We find that the equation is a first order linear differential equation.
Using the information in the tool box,
let us find the I.F
$\int Pdx =\int \large\frac{dx}{x }$$= \log x$
$I.F = e^{\large\log x} = x$
Step 2:
Hence the solution is $y.x = \int x^2.x dx + c$
$yx = \int x^3 dx + C$
$yx =\large\frac{ x^4}{4}$$ + C$
This is the required solution.
answered Aug 1, 2013 by sreemathi.v