58.1.39 problem 39

Internal problem ID [9110]
Book : Second order enumerated odes
Section : section 1
Problem number : 39
Date solved : Monday, January 27, 2025 at 05:42:10 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 14

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

\[ y = \sin \left (x \right ) c_{2} +\cos \left (x \right ) c_{1} +x \]

✓ Solution by Mathematica

Time used: 0.012 (sec). Leaf size: 17

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

\[ y(x)\to x+c_1 \cos (x)+c_2 \sin (x) \]