73.16.1 problem 24.1 (a)

Internal problem ID [15442]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 24. Variation of parameters. Additional exercises page 444
Problem number : 24.1 (a)
Date solved : Monday, March 31, 2025 at 01:37:54 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.006 (sec). Leaf size: 18

ode:=x^2*diff(diff(y(x),x),x)-2*x*diff(y(x),x)+2*y(x) = 3*x^(1/2); 
dsolve(ode,y(x), singsol=all);
 

\[ y = c_2 \,x^{2}+c_1 x +4 \sqrt {x} \]

✓ Mathematica. Time used: 0.016 (sec). Leaf size: 23

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

\[ y(x)\to c_2 x^2+4 \sqrt {x}+c_1 x \]

✓ Sympy. Time used: 0.330 (sec). Leaf size: 17

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

\[ y{\left (x \right )} = C_{1} x + C_{2} x^{2} + 4 \sqrt {x} \]