67.1.8 problem Problem 1(h)

Internal problem ID [13955]
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)
Date solved : Tuesday, January 28, 2025 at 06:09:38 AM
CAS classification : [_separable]

\begin{align*} y^{\prime }&=x \,{\mathrm e}^{y^{2}-x} \end{align*}

✓ Solution by Maple

Time used: 0.009 (sec). Leaf size: 23

dsolve(diff(y(x),x)=x*exp(y(x)^2-x),y(x), singsol=all)
 

\[ \left (-x -1\right ) {\mathrm e}^{-x}-\frac {\sqrt {\pi }\, \operatorname {erf}\left (y\right )}{2}+c_{1} = 0 \]

✓ Solution by Mathematica

Time used: 0.681 (sec). Leaf size: 28

DSolve[D[y[x],x]==x*Exp[y[x]^2-x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \text {erf}^{-1}\left (-\frac {2 e^{-x} \left (x-c_1 e^x+1\right )}{\sqrt {\pi }}\right ) \]