Internal problem ID [2029]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 11, page 45
Problem number: 19.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_1st_order, `_with_symmetry_[F(x),G(y)]`]]
\[ \boxed {y^{\prime }-x \left (1-{\mathrm e}^{-x^{2}+2 y}\right )=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.063 (sec). Leaf size: 18
dsolve([diff(y(x),x)=x*(1-exp(2*y(x)-x^2)),y(0) = 0],y(x), singsol=all)
\[ y = \frac {x^{2}}{2}-\frac {\ln \left (x^{2}+1\right )}{2} \]
✓ Solution by Mathematica
Time used: 0.5 (sec). Leaf size: 21
DSolve[{y'[x]==x*(1-Exp[2*y[x]-x^2]),{y[0]==0}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{2} \left (x^2-\log \left (x^2+1\right )\right ) \]