49.23.10 problem 5(c)

Internal problem ID [7768]
Book : An introduction to Ordinary Differential Equations. Earl A. Coddington. Dover. NY 1961
Section : Chapter 6. Existence and uniqueness of solutions to systems and nth order equations. Page 238
Problem number : 5(c)
Date solved : Monday, January 27, 2025 at 03:19:08 PM
CAS classification : [[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]

\begin{align*} y^{\prime \prime }+\sin \left (y\right )&=0 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=2 \end{align*}

✓ Solution by Maple

Time used: 1.681 (sec). Leaf size: 27

dsolve([diff(y(x),x$2)+sin(y(x))=0,y(0) = 0, D(y)(0) = 2],y(x), singsol=all)
 

\[ y = \operatorname {RootOf}\left (-\int _{0}^{\textit {\_Z}}\sec \left (\frac {\textit {\_a}}{2}\right ) \operatorname {csgn}\left (\cos \left (\frac {\textit {\_a}}{2}\right )\right )d \textit {\_a} +2 x \right ) \]

✗ Solution by Mathematica

Time used: 0.000 (sec). Leaf size: 0

DSolve[{D[y[x],{x,2}]+Sin[y[x]]==0,{y[0]==0,Derivative[1][y][0] ==2}},y[x],x,IncludeSingularSolutions -> True]
 

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