Final answer to the problem
$y=C_1xe^{\left(x^2\right)}$
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1
Apply the formula: $a\frac{dy}{dx}+c=f$$\to \frac{dy}{dx}+\frac{c}{a}=\frac{f}{a}$, where $a=x$, $c=-y$ and $f=2x^2y$
$\frac{dy}{dx}+\frac{-y}{x}=\frac{2x^2y}{x}$
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$\frac{dy}{dx}+\frac{-y}{x}=\frac{2x^2y}{x}$
Learn how to solve problems step by step online. xdy/dx-y=2x^2y. Apply the formula: a\frac{dy}{dx}+c=f\to \frac{dy}{dx}+\frac{c}{a}=\frac{f}{a}, where a=x, c=-y and f=2x^2y. Apply the formula: \frac{a^n}{a}=a^{\left(n-1\right)}, where a^n/a=\frac{2x^2y}{x}, a^n=x^2, a=x and n=2. Apply the formula: a+b=c\to a-c=-b, where a=\frac{dy}{dx}, b=\frac{-y}{x} and c=2xy. Apply the formula: -\frac{b}{c}=\frac{expand\left(-b\right)}{c}, where b=-y and c=x.
Final answer to the problem
$y=C_1xe^{\left(x^2\right)}$
