Internal problem ID [15038]
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: 136.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_1st_order, `_with_symmetry_[F(x)*G(y),0]`]]
\[ \boxed {\left (\frac {{\mathrm e}^{-y^{2}}}{2}-y x \right ) y^{\prime }=1} \]
✓ Solution by Maple
Time used: 0.046 (sec). Leaf size: 34
dsolve((exp(-(y(x)^2))/2-x*y(x))*diff(y(x),x)-1=0,y(x), singsol=all)
\[ \frac {\left (-\sqrt {\pi }\, \sqrt {2}\, \operatorname {erf}\left (\frac {\sqrt {2}\, y \left (x \right )}{2}\right )-4 c_{1} \right ) {\mathrm e}^{-\frac {y \left (x \right )^{2}}{2}}}{4}+x = 0 \]
✓ Solution by Mathematica
Time used: 0.211 (sec). Leaf size: 32
DSolve[(Exp[-(y[x]^2)/2]-x*y[x])*y'[x]-1==0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [x=e^{-\frac {1}{2} y(x)^2} y(x)+c_1 e^{-\frac {1}{2} y(x)^2},y(x)\right ] \]