Internal problem ID [2071]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 12, page 46
Problem number: 41.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {x \,{\mathrm e}^{-y^{2}}+y y^{\prime }=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 4.5 (sec). Leaf size: 29
dsolve([(x*exp(-y(x)^2))+y(x)*diff(y(x),x)=0,y(0) = 0],y(x), singsol=all)
\begin{align*} y \left (x \right ) &= \sqrt {\ln \left (-x^{2}+1\right )} \\ y \left (x \right ) &= -\sqrt {\ln \left (-x^{2}+1\right )} \\ \end{align*}
✓ Solution by Mathematica
Time used: 2.245 (sec). Leaf size: 35
DSolve[{(x*Exp[-y[x]^2])+y[x]*y'[x]==0,{y[0]==0}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\sqrt {\log \left (1-x^2\right )} \\ y(x)\to \sqrt {\log \left (1-x^2\right )} \\ \end{align*}