75.5.15 problem 114

Internal problem ID [16751]
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 : 114
Date solved : Tuesday, January 28, 2025 at 09:21:09 AM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} x -2 y-1+\left (3 x -6 y+2\right ) y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.082 (sec). Leaf size: 21

dsolve((x-2*y(x)-1)+(3*x-6*y(x)+2)*diff(y(x),x)=0,y(x), singsol=all)
 

\[ y = -\frac {\operatorname {LambertW}\left (-3 \,{\mathrm e}^{\frac {5 x}{2}-\frac {5 c_{1}}{2}}\right )}{3}+\frac {x}{2} \]

✓ Solution by Mathematica

Time used: 4.062 (sec). Leaf size: 38

DSolve[(x-2*y[x]-1)+(3*x-6*y[x]+2)*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \frac {1}{6} \left (3 x-2 W\left (-e^{\frac {5 x}{2}-1+c_1}\right )\right ) \\ y(x)\to \frac {x}{2} \\ \end{align*}