67.8.36 problem 13.6 (b)

Internal problem ID [16531]
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 (b)
Date solved : Thursday, October 02, 2025 at 01:36:06 PM
CAS classification : [[_2nd_order, _missing_y]]

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

With initial conditions

\begin{align*} y \left (-1\right )&=4 \\ y^{\prime }\left (-1\right )&=12 \\ \end{align*}

✓ Maple. Time used: 0.022 (sec). Leaf size: 11

ode:=x*diff(diff(y(x),x),x) = 2*diff(y(x),x); 
ic:=[y(-1) = 4, D(y)(-1) = 12]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = 4 x^{3}+8 \]

✓ Mathematica. Time used: 0.007 (sec). Leaf size: 12

ode=x*D[y[x],{x,2}]==2*D[y[x],x]; 
ic={y[-1]==4,Derivative[1][y][-1]==12}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to 4 \left (x^3+2\right ) \end{align*}

✓ Sympy. Time used: 0.079 (sec). Leaf size: 8

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x*Derivative(y(x), (x, 2)) - 2*Derivative(y(x), x),0) 
ics = {y(-1): 4, Subs(Derivative(y(x), x), x, -1): 12} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = 4 x^{3} + 8 \]