Internal problem ID [10871]
Book: APPLIED DIFFERENTIAL EQUATIONS The Primary Course by Vladimir A. Dobrushkin.
CRC Press 2015
Section: Chapter 2, First Order Equations. Problems page 149
Problem number: Problem 1(h).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {y^{\prime }-x \,{\mathrm e}^{-x +y^{2}}=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 22
dsolve(diff(y(x),x)=x*exp(y(x)^2-x),y(x), singsol=all)
\[ -\left (x +1\right ) {\mathrm e}^{-x}-\frac {\sqrt {\pi }\, \operatorname {erf}\left (y \left (x \right )\right )}{2}+c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.8 (sec). Leaf size: 28
DSolve[y'[x]==x*Exp[y[x]^2-x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \text {erf}^{-1}\left (-\frac {2 e^{-x} \left (x-c_1 e^x+1\right )}{\sqrt {\pi }}\right ) \\ \end{align*}