75.5.12 problem 111

Internal problem ID [16748]
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 : 111
Date solved : Tuesday, January 28, 2025 at 09:20:58 AM
CAS classification : [[_homogeneous, `class C`], _exact, _rational, [_Abel, `2nd type`, `class A`]]

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

✓ Solution by Maple

Time used: 1.700 (sec). Leaf size: 30

dsolve((x+y(x))+(x-y(x)-2)*diff(y(x),x)=0,y(x), singsol=all)
 

\[ y = \frac {-\sqrt {2 \left (x -1\right )^{2} c_{1}^{2}+1}+c_{1} \left (x -2\right )}{c_{1}} \]

✓ Solution by Mathematica

Time used: 0.124 (sec). Leaf size: 59

DSolve[(x+y[x])+(x-y[x]-2)*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -i \sqrt {-2 x^2+4 x-4-c_1}+x-2 \\ y(x)\to i \sqrt {-2 x^2+4 x-4-c_1}+x-2 \\ \end{align*}