Internal problem ID [2107]
Book: Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition,
2015
Section: Chapter 1, First-Order Differential Equations. Section 1.2, Basic Ideas and Terminology. page
21
Problem number: Problem 38.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _quadrature]]
Solve \begin {gather*} \boxed {y^{\prime \prime }-\cos \relax (x )=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 2, y^{\prime }\relax (0) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.012 (sec). Leaf size: 11
dsolve([diff(y(x),x$2)=cos(x),y(0) = 2, D(y)(0) = 1],y(x), singsol=all)
\[ y \relax (x ) = -\cos \relax (x )+x +3 \]
✓ Solution by Mathematica
Time used: 0.007 (sec). Leaf size: 12
DSolve[{y''[x]==Cos[x],{y[0]==2,y'[0]==1}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x-\cos (x)+3 \\ \end{align*}