89.33.24 problem 26

Internal problem ID [25008]
Book : A short course in Differential Equations. Earl D. Rainville. Second edition. 1958. Macmillan Publisher, NY. CAT 58-5010
Section : Chapter 17. Special Equations of order Two. Exercises at page 251
Problem number : 26
Date solved : Thursday, October 02, 2025 at 11:46:48 PM
CAS classification : [[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]]

\begin{align*} 2 y^{\prime \prime }&={y^{\prime }}^{3} \sin \left (2 x \right ) \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=1 \\ y^{\prime }\left (0\right )&=1 \\ \end{align*}

✓ Maple. Time used: 0.461 (sec). Leaf size: 9

ode:=2*diff(diff(y(x),x),x) = diff(y(x),x)^3*sin(2*x); 
ic:=[y(0) = 1, D(y)(0) = 1]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = \operatorname {InverseJacobiAM}\left (x , 1\right )+1 \]

✓ Mathematica. Time used: 45.382 (sec). Leaf size: 10

ode=2*D[y[x],{x,2}]==D[y[x],x]^3*Sin[2*x]; 
ic={y[0]==1,Derivative[1][y][0] ==1}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \operatorname {EllipticF}(x,1)+1 \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-sin(2*x)*Derivative(y(x), x)**3 + 2*Derivative(y(x), (x, 2)),0) 
ics = {y(0): 1, Subs(Derivative(y(x), x), x, 0): 1} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out