Internal problem ID [6100]
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).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]
\[ \boxed {y^{\prime \prime }+\sin \left (y\right )=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 0, y^{\prime }\left (0\right ) = 2] \end {align*}
✓ Solution by Maple
Time used: 1.296 (sec). Leaf size: 23
dsolve([diff(y(x),x$2)+sin(y(x))=0,y(0) = 0, D(y)(0) = 2],y(x), singsol=all)
\[ y \left (x \right ) = \operatorname {RootOf}\left (-\left (\int _{0}^{\textit {\_Z}}\sec \left (\frac {\textit {\_a}}{2}\right ) \operatorname {csgn}\left (\cos \left (\frac {\textit {\_a}}{2}\right )\right )d \textit {\_a} \right )+2 x \right ) \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[{y''[x]+Sin[y[x]]==0,{y[0]==0,y'[0]==2}},y[x],x,IncludeSingularSolutions -> True]
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