60.1.219 problem 224

Internal problem ID [10233]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 224
Date solved : Wednesday, March 05, 2025 at 08:45:40 AM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

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

✓ Maple. Time used: 0.027 (sec). Leaf size: 23

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

\[ y = -\frac {2 \operatorname {LambertW}\left (-\frac {{\mathrm e}^{\frac {25 x}{4}-1-\frac {25 c_{1}}{4}}}{2}\right )}{5}+3 x -\frac {2}{5} \]

✓ Mathematica. Time used: 3.209 (sec). Leaf size: 40

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

\begin{align*} y(x)\to 3 x-\frac {2}{5} \left (1+W\left (-e^{\frac {25 x}{4}-1+c_1}\right )\right ) \\ y(x)\to 3 x-\frac {2}{5} \\ \end{align*}

✓ Sympy. Time used: 3.804 (sec). Leaf size: 122

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

\[ \left [ y{\left (x \right )} = 3 x - \frac {2 W\left (- \frac {\sqrt [4]{C_{1} e^{25 x}}}{2 e}\right )}{5} - \frac {2}{5}, \ y{\left (x \right )} = 3 x - \frac {2 W\left (\frac {\sqrt [4]{C_{1} e^{25 x}}}{2 e}\right )}{5} - \frac {2}{5}, \ y{\left (x \right )} = 3 x - \frac {2 W\left (- \frac {i \sqrt [4]{C_{1} e^{25 x}}}{2 e}\right )}{5} - \frac {2}{5}, \ y{\left (x \right )} = 3 x - \frac {2 W\left (\frac {i \sqrt [4]{C_{1} e^{25 x}}}{2 e}\right )}{5} - \frac {2}{5}\right ] \]