60.1.221 problem 226

Internal problem ID [10235]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 226
Date solved : Sunday, March 30, 2025 at 03:33:15 PM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} \left (4 y-2 x -3\right ) y^{\prime }+2 y-x -1&=0 \end{align*}

✓ Maple. Time used: 0.019 (sec). Leaf size: 21

ode:=(4*y(x)-2*x-3)*diff(y(x),x)+2*y(x)-x-1 = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {x}{2}-\frac {\operatorname {LambertW}\left (-c_1 \,{\mathrm e}^{5+8 x}\right )}{8}+\frac {5}{8} \]

✓ Mathematica. Time used: 0.11 (sec). Leaf size: 41

ode=(4*y[x]-2*x-3)*D[y[x],x]+2*y[x]-x-1==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)\to \frac {1}{8} \left (-W\left (-e^{8 x-1+c_1}\right )+4 x+5\right ) \\ y(x)\to \frac {1}{8} (4 x+5) \\ \end{align*}

✓ Sympy. Time used: 0.995 (sec). Leaf size: 20

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x + (-2*x + 4*y(x) - 3)*Derivative(y(x), x) + 2*y(x) - 1,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {x}{2} - \frac {W\left (C_{1} e^{8 x + 5}\right )}{8} + \frac {5}{8} \]