71.6.4 problem 4

Internal problem ID [14410]
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
Date solved : Tuesday, January 28, 2025 at 06:29:58 AM
CAS classification : [_separable]

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

With initial conditions

\begin{align*} y \left (0\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.069 (sec). Leaf size: 19

dsolve([diff(y(x),x)=x*exp(y(x)-x^2),y(0) = 0],y(x), singsol=all)
 

\[ y = \ln \left (2\right )-\ln \left ({\mathrm e}^{x^{2}}+1\right )+x^{2} \]

✓ Solution by Mathematica

Time used: 2.089 (sec). Leaf size: 21

DSolve[{D[y[x],x]==x*Exp[y[x]-x^2],{y[0]==0}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -\log \left (\frac {1}{2} \left (e^{-x^2}+1\right )\right ) \]