Internal problem ID [6086]
Book: Elementary differential equations. By Earl D. Rainville, Phillip E. Bedient. Macmilliam
Publishing Co. NY. 6th edition. 1981.
Section: CHAPTER 16. Nonlinear equations. Section 101. Independent variable missing. EXERCISES
Page 324
Problem number: 20.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]
Solve \begin {gather*} \boxed {2 y^{\prime \prime }-\sin \left (2 y\right )=0} \end {gather*} With initial conditions \begin {align*} \left [y \relax (0) = \frac {\pi }{2}, y^{\prime }\relax (0) = 1\right ] \end {align*}
✗ Solution by Maple
dsolve([2*diff(y(x),x$2)=sin(2*y(x)),y(0) = 1/2*Pi, D(y)(0) = 1],y(x), singsol=all)
\[ \text {No solution found} \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[{2*y''[x]==Sin[2*y[x]],{y[0]==Pi/2,y'[0]==1}},y[x],x,IncludeSingularSolutions -> True]
{}