# Find an explicit particular sol'n of the initial value problem x*(dx/dy)-y=2x^2 *y.

Find an explicit particular sol'n of the initial value problem $x\ast \left(dx/dy\right)-y=2{x}^{2}\ast y$
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Jamarion Roth
$x\ast \left(dx/dy\right)-y=2{x}^{2}\ast y$
$x{y}^{\prime }=y\left(1+2{x}^{2}\right)$
${y}^{\prime }/y=\left(1+2{x}^{2}\right)/x$ this is a separable diff. eqn.
$\frac{dy}{y}=\frac{\left(1+2{x}^{2}\right)}{x}dx$
$\int \frac{dy}{y}dy=\int \frac{\left(1+2{x}^{2}\right)}{x}dx=\int \left(\frac{1}{x}+2x\right)dx$
$\mathrm{ln}\left(y\right)=\mathrm{ln}\left(x\right)+{x}^{2}+c$