15.16.5 problem 5

Internal problem ID [3225]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 25, page 112
Problem number : 5
Date solved : Tuesday, March 04, 2025 at 04:06:39 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} 2 x^{2} y^{\prime \prime }-3 x y^{\prime }-18 y&=\ln \left (x \right ) \end{align*}

✓ Maple. Time used: 0.005 (sec). Leaf size: 20

ode:=2*x^2*diff(diff(y(x),x),x)-3*x*diff(y(x),x)-18*y(x) = ln(x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = x^{{9}/{2}} c_2 +\frac {c_{1}}{x^{2}}-\frac {\ln \left (x \right )}{18}+\frac {5}{324} \]

✓ Mathematica. Time used: 0.029 (sec). Leaf size: 29

ode=2*x^2*D[y[x],{x,2}]-3*x*D[y[x],x]-18*y[x]==Log[x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to c_2 x^{9/2}+\frac {c_1}{x^2}-\frac {\log (x)}{18}+\frac {5}{324} \]

✓ Sympy. Time used: 0.245 (sec). Leaf size: 22

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(2*x**2*Derivative(y(x), (x, 2)) - 3*x*Derivative(y(x), x) - 18*y(x) - log(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {C_{1}}{x^{2}} + C_{2} x^{\frac {9}{2}} - \frac {\log {\left (x \right )}}{18} + \frac {5}{324} \]