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# Find the general solution of the differential equation$\large\frac{dy}{dx}+\frac{y}{x}$$=x^2 Can you answer this question? ## 1 Answer 0 votes Toolbox: • To solve the first order linear differential equation of the form \large\frac{dy}{dx}$$ + Py = Q$
• (i) Write the given equation in the form of $\large\frac{dy}{dx}$$+ Py = Q • (ii) Find the integrating factor (I.F) = e^{\int Pdx}. • (iii) Write the solution as y(I.F) = integration of Q(I.F) dx + C Step 1: We find that the equation is a first order linear differential equation. Using the information in the tool box, let us find the I.F \int Pdx =\int \large\frac{dx}{x }$$= \log x$
$I.F = e^{\large\log x} = x$
Step 2:
Hence the solution is $y.x = \int x^2.x dx + c$
$yx = \int x^3 dx + C$