Internal problem ID [12674]
Book: Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section: Chapter 2. The Initial Value Problem. Exercises 2.3.2, page 63
Problem number: 4.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {y^{\prime }-x \,{\mathrm e}^{-x^{2}+y}=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.062 (sec). Leaf size: 19
dsolve([diff(y(x),x)=x*exp(y(x)-x^2),y(0) = 0],y(x), singsol=all)
\[ y \left (x \right ) = \ln \left (2\right )-\ln \left (1+{\mathrm e}^{x^{2}}\right )+x^{2} \]
✓ Solution by Mathematica
Time used: 2.198 (sec). Leaf size: 21
DSolve[{y'[x]==x*Exp[y[x]-x^2],{y[0]==0}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -\log \left (\frac {1}{2} \left (e^{-x^2}+1\right )\right ) \]