Question

For each the differential equations given, find the general solution :
$\frac{dy}{dx}+\frac{y}{x}=x^2$

Answer 1

$\frac{dy}{dx}+\frac{y}{x}=x^2$

$\frac{dy}{dx}+Py=Q$

$P=\frac{1}{x},Q=x^2$

$I.F.=e^{\int Pdx}$

$=e^{\int \frac{1}{x}dx}$

$=e^{\ln x}=x$

$y\times I.F=\int Q\times I.Fdx+c$

$y\times x=\int (x^2\times x)dx+c$

$yx=\int x^{3}dx+c$

$yx=\frac{x^4}{4}+c$