75.6.12 problem 136

Internal problem ID [16768]
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
Date solved : Tuesday, January 28, 2025 at 09:21:54 AM
CAS classification : [[_1st_order, `_with_symmetry_[F(x)*G(y),0]`]]

\begin{align*} \left (\frac {{\mathrm e}^{-y^{2}}}{2}-y x \right ) y^{\prime }-1&=0 \end{align*}

✓ Solution by Maple

Time used: 0.421 (sec). Leaf size: 34

dsolve((exp(-(y(x)^2))/2-x*y(x))*diff(y(x),x)-1=0,y(x), singsol=all)
 

\[ \frac {\left (-\sqrt {\pi }\, \sqrt {2}\, \operatorname {erf}\left (\frac {\sqrt {2}\, y}{2}\right )-4 c_{1} \right ) {\mathrm e}^{-\frac {y^{2}}{2}}}{4}+x = 0 \]

✓ Solution by Mathematica

Time used: 0.228 (sec). Leaf size: 32

DSolve[(Exp[-(y[x]^2)/2]-x*y[x])*D[y[x],x]-1==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [x=e^{-\frac {1}{2} y(x)^2} y(x)+c_1 e^{-\frac {1}{2} y(x)^2},y(x)\right ] \]