9.3.15 problem 15

Internal problem ID [2908]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 7, page 28
Problem number : 15
Date solved : Tuesday, September 30, 2025 at 06:05:00 AM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

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

With initial conditions

\begin{align*} y \left (3\right )&=1 \\ \end{align*}

✓ Maple. Time used: 0.170 (sec). Leaf size: 20

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

\[ y = \frac {7}{3}-\frac {2 x}{3}+3 \operatorname {LambertW}\left (\frac {2 \,{\mathrm e}^{\frac {5}{9}-\frac {x}{9}}}{9}\right ) \]

✓ Mathematica. Time used: 2.377 (sec). Leaf size: 32

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

\begin{align*} y(x)&\to \frac {1}{3} \left (9 W\left (\frac {2}{9} e^{\frac {5}{9}-\frac {x}{9}}\right )-2 x+7\right ) \end{align*}

✓ Sympy. Time used: 42.479 (sec). Leaf size: 44

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

\[ y{\left (x \right )} = - \frac {2 x}{3} + 3 W\left (\frac {2 \sqrt [9]{- e^{- x}} e^{\frac {4}{3}} e^{- \frac {7}{9} - \frac {i \pi }{9}}}{9}\right ) + \frac {7}{3} \]