15.16.7 problem 7

Internal problem ID [3227]
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 : 7
Date solved : Sunday, March 30, 2025 at 01:21:54 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.004 (sec). Leaf size: 15

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

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

✓ Mathematica. Time used: 0.022 (sec). Leaf size: 19

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

\[ y(x)\to x^2 (x+2 c_2 \log (x)+c_1) \]

✓ Sympy. Time used: 0.215 (sec). Leaf size: 14

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

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