73.1.21 problem 2.3 (k)

Internal problem ID [14928]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 2. Integration and differential equations. Additional exercises. page 32
Problem number : 2.3 (k)
Date solved : Monday, March 31, 2025 at 01:04:12 PM
CAS classification : [[_2nd_order, _quadrature]]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 19

ode:=diff(diff(y(x),x),x)-3 = x; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {1}{6} x^{3}+\frac {3}{2} x^{2}+c_1 x +c_2 \]

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 26

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

\[ y(x)\to \frac {x^3}{6}+\frac {3 x^2}{2}+c_2 x+c_1 \]

✓ Sympy. Time used: 0.060 (sec). Leaf size: 19

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

\[ y{\left (x \right )} = C_{1} + C_{2} x + \frac {x^{3}}{6} + \frac {3 x^{2}}{2} \]