29.7.16 problem 19

Internal problem ID [7333]
Book : Mathematical Methods in the Physical Sciences. third edition. Mary L. Boas. John Wiley. 2006
Section : Chapter 8, Ordinary differential equations. Section 7. Other second-Order equations. page 435
Problem number : 19
Date solved : Tuesday, September 30, 2025 at 04:29:08 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{2} y^{\prime \prime }-5 x y^{\prime }+9 y&=2 x^{3} \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 18

ode:=x^2*diff(diff(y(x),x),x)-5*x*diff(y(x),x)+9*y(x) = 2*x^3; 
dsolve(ode,y(x), singsol=all);
 

\[ y = x^{3} \left (c_2 +c_1 \ln \left (x \right )+\ln \left (x \right )^{2}\right ) \]

✓ Mathematica. Time used: 0.014 (sec). Leaf size: 22

ode=x^2*D[y[x],{x,2}]-5*x*D[y[x],x]+9*y[x]==2*x^3; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to x^3 \left (\log ^2(x)+3 c_2 \log (x)+c_1\right ) \end{align*}

✓ Sympy. Time used: 0.154 (sec). Leaf size: 17

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-2*x**3 + x**2*Derivative(y(x), (x, 2)) - 5*x*Derivative(y(x), x) + 9*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = x^{3} \left (C_{1} + C_{2} \log {\left (x \right )} + \log {\left (x \right )}^{2}\right ) \]