75.5.15 problem 114

Internal problem ID [16680]
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 : Monday, March 31, 2025 at 03:05:15 PM
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*}

✓ Maple. Time used: 0.026 (sec). Leaf size: 21

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

\[ y = -\frac {\operatorname {LambertW}\left (-3 \,{\mathrm e}^{\frac {5 x}{2}-\frac {5 c_1}{2}}\right )}{3}+\frac {x}{2} \]

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

ode=(x-2*y[x]-1)+(3*x-6*y[x]+2)*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},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*}

✓ Sympy. Time used: 1.465 (sec). Leaf size: 42

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x + (3*x - 6*y(x) + 2)*Derivative(y(x), x) - 2*y(x) - 1,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ \left [ y{\left (x \right )} = \frac {x}{2} - \frac {W\left (- 3 \sqrt {C_{1} e^{5 x}}\right )}{3}, \ y{\left (x \right )} = \frac {x}{2} - \frac {W\left (3 \sqrt {C_{1} e^{5 x}}\right )}{3}\right ] \]