48.3.16 problem Example 3.45

Internal problem ID [7540]
Book : THEORY OF DIFFERENTIAL EQUATIONS IN ENGINEERING AND MECHANICS. K.T. CHAU, CRC Press. Boca Raton, FL. 2018
Section : Chapter 3. Ordinary Differential Equations. Section 3.5 HIGHER ORDER ODE. Page 181
Problem number : Example 3.45
Date solved : Monday, January 27, 2025 at 03:04:53 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.003 (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]
 

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