67.8.41 problem 13.6 (g)

Internal problem ID [16536]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 13. Higher order equations: Extending first order concepts. Additional exercises page 259
Problem number : 13.6 (g)
Date solved : Thursday, October 02, 2025 at 01:36:10 PM
CAS classification : [[_2nd_order, _missing_y]]

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

With initial conditions

\begin{align*} y \left (1\right )&=4 \\ y^{\prime }\left (1\right )&=5 \\ \end{align*}

✓ Maple. Time used: 0.025 (sec). Leaf size: 14

ode:=x*diff(diff(y(x),x),x)+2*diff(y(x),x) = 6; 
ic:=[y(1) = 4, D(y)(1) = 5]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = -\frac {2}{x}+3 x +3 \]

✓ Mathematica. Time used: 0.008 (sec). Leaf size: 15

ode=x*D[y[x],{x,2}]+2*D[y[x],x]==6; 
ic={y[1]==4,Derivative[1][y][1]==5}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to 3 x-\frac {2}{x}+3 \end{align*}

✓ Sympy. Time used: 0.122 (sec). Leaf size: 10

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x*Derivative(y(x), (x, 2)) + 2*Derivative(y(x), x) - 6,0) 
ics = {y(1): 4, Subs(Derivative(y(x), x), x, 1): 5} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = 3 x + 3 - \frac {2}{x} \]