81.7.1 problem 2

Internal problem ID [18698]
Book : A short course on differential equations. By Donald Francis Campbell. Maxmillan company. London. 1907
Section : Chapter VI. Certain particular forms of equations. Exercises at page 74
Problem number : 2
Date solved : Tuesday, January 28, 2025 at 12:10:42 PM
CAS classification : [[_2nd_order, _quadrature]]

\begin{align*} y^{\prime \prime }&=\cos \left (x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 13

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

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

✓ Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 16

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

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