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 : Monday, January 27, 2025 at 07:23:39 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

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

dsolve(diff(y(x),x$2)+4*y(x)=x^2,y(x), singsol=all)
 

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

✓ Solution by Mathematica

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

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

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