75.5.9 problem 108

Internal problem ID [16745]
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 : 108
Date solved : Tuesday, January 28, 2025 at 09:20:49 AM
CAS classification : [_linear]

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

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 19

dsolve(x+y(x)-2+(1-x)*diff(y(x),x)=0,y(x), singsol=all)
 

\[ y = \ln \left (x -1\right ) \left (x -1\right )+1+c_{1} \left (x -1\right ) \]

✓ Solution by Mathematica

Time used: 0.042 (sec). Leaf size: 27

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

\[ y(x)\to (x-1) \log (1-x)+(-1+c_1) x+2-c_1 \]