67.8.29 problem 13.5 (e)

Internal problem ID [16524]
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 : 13.5 (e)
Date solved : Thursday, October 02, 2025 at 01:36:01 PM
CAS classification : [[_2nd_order, _missing_y]]

\begin{align*} -y^{\prime }+x y^{\prime \prime }&=6 x^{5} \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 17

ode:=x*diff(diff(y(x),x),x)-diff(y(x),x) = 6*x^5; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {1}{4} x^{6}+\frac {1}{2} c_1 \,x^{2}+c_2 \]

✓ Mathematica. Time used: 0.019 (sec). Leaf size: 24

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

\begin{align*} y(x)&\to \frac {1}{4} \left (x^6+2 c_1 x^2+4 c_2\right ) \end{align*}

✓ Sympy. Time used: 0.182 (sec). Leaf size: 14

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

\[ y{\left (x \right )} = C_{1} + C_{2} x^{2} + \frac {x^{6}}{4} \]