Internal problem ID [15062]
Book: A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV,
G.I. MARKARENKO. MIR, MOSCOW. 1983
Section: Section 6. Linear equations of the first order. The Bernoulli equation. Exercises page
54
Problem number: 169.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [`y=_G(x,y')`]
\[ \boxed {y y^{\prime }-\left (x -1\right ) {\mathrm e}^{-\frac {y^{2}}{2}}=-1} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 42
dsolve(y(x)*diff(y(x),x)+1=(x-1)*exp(-y(x)^2/2),y(x), singsol=all)
\begin{align*} y \left (x \right ) &= \sqrt {2}\, \sqrt {\ln \left (-c_{1} {\mathrm e}^{-x}+x -2\right )} \\ y \left (x \right ) &= -\sqrt {2}\, \sqrt {\ln \left (-c_{1} {\mathrm e}^{-x}+x -2\right )} \\ \end{align*}
✓ Solution by Mathematica
Time used: 7.375 (sec). Leaf size: 60
DSolve[y[x]*y'[x]+1==(x-1)*Exp[-y[x]^2/2],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\sqrt {2} \sqrt {-x+\log \left (e^x (x-2)+c_1\right )} \\ y(x)\to \sqrt {2} \sqrt {-x+\log \left (e^x (x-2)+c_1\right )} \\ \end{align*}