87.9.5 problem 20

Internal problem ID [23378]
Book : Ordinary differential equations with modern applications. Ladas, G. E. and Finizio, N. Wadsworth Publishing. California. 1978. ISBN 0-534-00552-7. QA372.F56
Section : Chapter 2. Linear differential equations. Exercise at page 74
Problem number : 20
Date solved : Thursday, October 02, 2025 at 09:40:48 PM
CAS classification : [[_2nd_order, _quadrature]]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 14

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

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

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

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

\begin{align*} y(x)&\to \frac {x^3}{2}+c_2 x+c_1 \end{align*}

✓ Sympy. Time used: 0.039 (sec). Leaf size: 12

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

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