75.5.8 problem 107

Internal problem ID [16744]
Book : A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV, G.I. MARKARENKO. MIR, MOSCOW. 1983
Section : Section 5. Homogeneous equations. Exercises page 44
Problem number : 107
Date solved : Tuesday, January 28, 2025 at 09:20:44 AM
CAS classification : [[_homogeneous, `class A`], _exact, _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} y-x +\left (x +y\right ) y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.150 (sec). Leaf size: 51

dsolve((y(x)-x)+(y(x)+x)*diff(y(x),x)=0,y(x), singsol=all)
 

\begin{align*} y &= \frac {-c_{1} x -\sqrt {2 c_{1}^{2} x^{2}+1}}{c_{1}} \\ y &= \frac {-c_{1} x +\sqrt {2 c_{1}^{2} x^{2}+1}}{c_{1}} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.457 (sec). Leaf size: 94

DSolve[(y[x]-x)+(y[x]+x)*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -x-\sqrt {2 x^2+e^{2 c_1}} \\ y(x)\to -x+\sqrt {2 x^2+e^{2 c_1}} \\ y(x)\to -\sqrt {2} \sqrt {x^2}-x \\ y(x)\to \sqrt {2} \sqrt {x^2}-x \\ \end{align*}