15.16.6 problem 6

Internal problem ID [3226]
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 : 6
Date solved : Tuesday, March 04, 2025 at 04:06:41 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 23

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

\[ y = \frac {5}{2}+\frac {\ln \left (x^{2}\right )}{2}+\frac {2 c_{1} x^{2}}{3}+\sqrt {x}\, c_2 \]

✓ Mathematica. Time used: 0.03 (sec). Leaf size: 30

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

\[ y(x)\to \frac {1}{2} \left (\log \left (x^2\right )+5\right )+c_2 x^2+c_1 \sqrt {x} \]

✓ Sympy. Time used: 0.319 (sec). Leaf size: 20

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) + 2*y(x) - log(x**2),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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