73.17.43 problem 43

Internal problem ID [15506]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 25. Review exercises for part III. page 447
Problem number : 43
Date solved : Monday, March 31, 2025 at 01:39:50 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{2} y^{\prime \prime }+3 x y^{\prime }+2 y&=6 \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 22

ode:=x^2*diff(diff(y(x),x),x)+3*x*diff(y(x),x)+2*y(x) = 6; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {\sin \left (\ln \left (x \right )\right ) c_2 +\cos \left (\ln \left (x \right )\right ) c_1 +3 x}{x} \]

✓ Mathematica. Time used: 0.025 (sec). Leaf size: 25

ode=x^2*D[y[x],{x,2}]+3*x*D[y[x],x]+2*y[x]==6; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {3 x+c_2 \cos (\log (x))+c_1 \sin (\log (x))}{x} \]

✓ Sympy. Time used: 0.283 (sec). Leaf size: 20

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**2*Derivative(y(x), (x, 2)) + 3*x*Derivative(y(x), x) + 2*y(x) - 6,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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