15.3.12 problem 12

Internal problem ID [2905]
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 : 12
Date solved : Sunday, March 30, 2025 at 12:49:09 AM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} 6 x -3 y+6+\left (2 x -y+5\right ) y^{\prime }&=0 \end{align*}

With initial conditions

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

✓ Maple. Time used: 0.205 (sec). Leaf size: 20

ode:=6*x-3*y(x)+6+(2*x-y(x)+5)*diff(y(x),x) = 0; 
ic:=y(-1) = 1; 
dsolve([ode,ic],y(x), singsol=all);
 

\[ y = \frac {16}{5}-\frac {9 \operatorname {LambertW}\left (\frac {{\mathrm e}^{\frac {25 x}{9}+\frac {26}{9}}}{9}\right )}{5}+2 x \]

✓ Mathematica. Time used: 3.739 (sec). Leaf size: 32

ode=3*(2*x-y[x]+2)+(2*x-y[x]+5)*D[y[x],x]==0; 
ic={y[-1]==1}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to -\frac {9}{5} W\left (\frac {1}{9} e^{\frac {25 x}{9}+\frac {26}{9}}\right )+2 x+\frac {16}{5} \]

✓ Sympy. Time used: 68.494 (sec). Leaf size: 29

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(6*x + (2*x - y(x) + 5)*Derivative(y(x), x) - 3*y(x) + 6,0) 
ics = {y(-1): 1} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = 2 x - \frac {9 W\left (\frac {e^{\frac {26}{9}} \sqrt [9]{e^{25 x}}}{9}\right )}{5} + \frac {16}{5} \]