82.39.9 problem Ex. 9

Internal problem ID [18870]
Book : Introductory Course On Differential Equations by Daniel A Murray. Longmans Green and Co. NY. 1924
Section : Chapter VII. Linear equations with variable coefficients. End of chapter problems at page 91
Problem number : Ex. 9
Date solved : Monday, March 31, 2025 at 06:17:37 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y&=x^{m} \end{align*}

✓ Maple. Time used: 0.007 (sec). Leaf size: 26

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

\[ y = c_2 \,x^{2}+x^{2} \ln \left (x \right ) c_1 +\frac {x^{m}}{\left (m -2\right )^{2}} \]

✓ Mathematica. Time used: 0.041 (sec). Leaf size: 30

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

\[ y(x)\to \frac {x^m}{(m-2)^2}+c_1 x^2+2 c_2 x^2 \log (x) \]

✓ Sympy. Time used: 0.351 (sec). Leaf size: 36

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

\[ y{\left (x \right )} = \frac {x^{2} \left (C_{1} + C_{2} \log {\left (x \right )}\right ) \left (m^{2} - 4 m + 4\right ) + e^{m \log {\left (x \right )}}}{m^{2} - 4 m + 4} \]