75.5.16 problem 115

Internal problem ID [16752]
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 : 115
Date solved : Tuesday, January 28, 2025 at 09:21:11 AM
CAS classification : [[_homogeneous, `class C`], _exact, _rational, [_Abel, `2nd type`, `class A`]]

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

✓ Solution by Maple

Time used: 0.033 (sec). Leaf size: 39

dsolve((x+y(x))+(x+y(x)-1)*diff(y(x),x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.118 (sec). Leaf size: 43

DSolve[(x+y[x])+(x+y[x]-1)*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -x-\sqrt {-2 x+1+c_1}+1 \\ y(x)\to -x+\sqrt {-2 x+1+c_1}+1 \\ \end{align*}