15.20.16 problem 16

Internal problem ID [3324]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 38, page 173
Problem number : 16
Date solved : Tuesday, March 04, 2025 at 04:35:29 PM
CAS classification : [[_1st_order, _with_linear_symmetries], _dAlembert]

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

✓ Maple. Time used: 0.010 (sec). Leaf size: 766

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

\begin{align*} \text {Solution too large to show}\end{align*}

✓ Mathematica. Time used: 0.908 (sec). Leaf size: 137

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

\begin{align*} \text {Solve}\left [\frac {1}{2} \left (2 W\left (-\frac {3}{2} \sqrt {x^2 e^{2 y(x)-4}}\right )-\log \left (2 W\left (-\frac {3}{2} \sqrt {x^2 e^{2 y(x)-4}}\right )+3\right )+3\right )-y(x)&=c_1,y(x)\right ] \\ \text {Solve}\left [\frac {1}{2} \left (2 W\left (\frac {3}{2} \sqrt {x^2 e^{2 y(x)-4}}\right )-\log \left (2 W\left (\frac {3}{2} \sqrt {x^2 e^{2 y(x)-4}}\right )+3\right )+3\right )-y(x)&=c_1,y(x)\right ] \\ \end{align*}

✗ Sympy

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

NotImplementedError : The given ODE Derivative(y(x), x) - 2*LambertW(3*x*exp(y(x) - 2)/2)/(3*x) cannot be solved by the factorable group method