53.4.19 problem 20

Internal problem ID [8507]
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
Date solved : Monday, January 27, 2025 at 04:08:29 PM
CAS classification : [[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]

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

With initial conditions

\begin{align*} y \left (0\right )&=\frac {\pi }{2}\\ y^{\prime }\left (0\right )&=1 \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: 0.000 (sec). Leaf size: 0

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

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