15.12.3 problem 3

Internal problem ID [3147]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 20, page 90
Problem number : 3
Date solved : Tuesday, March 04, 2025 at 04:03:24 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }+4 y&=x^{2} \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 23

ode:=diff(diff(y(x),x),x)+4*y(x) = x^2; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \sin \left (2 x \right ) c_2 +\cos \left (2 x \right ) c_{1} +\frac {x^{2}}{4}-\frac {1}{8} \]

✓ Mathematica. Time used: 0.016 (sec). Leaf size: 30

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

\[ y(x)\to \frac {x^2}{4}+c_1 \cos (2 x)+c_2 \sin (2 x)-\frac {1}{8} \]

✓ Sympy. Time used: 0.073 (sec). Leaf size: 24

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

\[ y{\left (x \right )} = C_{1} \sin {\left (2 x \right )} + C_{2} \cos {\left (2 x \right )} + \frac {x^{2}}{4} - \frac {1}{8} \]