22.13 problem 13

Internal problem ID [2376]

Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section: Exercise 40, page 186
Problem number: 13.
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*} \left [y \left (0\right ) = \frac {\pi }{4}, y^{\prime }\left (0\right ) = 0\right ] \end {align*}

With the expansion point for the power series method at \(x = \frac {\pi }{4}\).

Solution by Maple

Order:=7; 
dsolve([diff(y(x),x$2)=sin(y(x)),y(0) = 1/4*Pi, D(y)(0) = 0],y(x),type='series',x=Pi/4);
 

\[ \text {No solution found} \]

Solution by Mathematica

Time used: 0.0 (sec). Leaf size: 0

AsymptoticDSolveValue[{y''[x]==Sin[y[x]],{y[0]==Pi/4,y'[0]==0}},y[x],{x,Pi/4,6}]
 

Not solved