75.5.11 problem 110

Internal problem ID [16747]
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 : 110
Date solved : Tuesday, January 28, 2025 at 09:20:55 AM
CAS classification : [[_homogeneous, `class C`], _exact, _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} x +y-2+\left (x -y+4\right ) y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 1.742 (sec). Leaf size: 30

dsolve((x+y(x)-2)+(x-y(x)+4)*diff(y(x),x)=0,y(x), singsol=all)
 

\[ y = \frac {-\sqrt {2 \left (x +1\right )^{2} c_{1}^{2}+1}+\left (x +4\right ) c_{1}}{c_{1}} \]

✓ Solution by Mathematica

Time used: 0.128 (sec). Leaf size: 59

DSolve[(x+y[x]-2)+(x-y[x]+4)*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -i \sqrt {-2 x^2-4 x-16-c_1}+x+4 \\ y(x)\to i \sqrt {-2 x^2-4 x-16-c_1}+x+4 \\ \end{align*}