75.12.20 problem 294

Internal problem ID [16886]
Book : A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV, G.I. MARKARENKO. MIR, MOSCOW. 1983
Section : Section 12. Miscellaneous problems. Exercises page 93
Problem number : 294
Date solved : Tuesday, January 28, 2025 at 09:39:42 AM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} x -y+2+\left (x -y+3\right ) y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.085 (sec). Leaf size: 19

dsolve((x-y(x)+2)+(x-y(x)+3)*diff(y(x),x)=0,y(x), singsol=all)
 

\[ y = x -\frac {\operatorname {LambertW}\left (-c_{1} {\mathrm e}^{5+4 x}\right )}{2}+\frac {5}{2} \]

✓ Solution by Mathematica

Time used: 3.568 (sec). Leaf size: 35

DSolve[(x-y[x]+2)+(x-y[x]+3)*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\frac {1}{2} W\left (-e^{4 x-1+c_1}\right )+x+\frac {5}{2} \\ y(x)\to x+\frac {5}{2} \\ \end{align*}