15.18.37 problem 37

Internal problem ID [3280]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 35, page 157
Problem number : 37
Date solved : Sunday, March 30, 2025 at 01:29:46 AM
CAS classification : [[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]]

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

With initial conditions

\begin{align*} y \left (0\right )&=0\\ y^{\prime }\left (0\right )&={\frac {1}{2}} \end{align*}

✗ Maple

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

\[ \text {No solution found} \]

✓ Mathematica. Time used: 1.878 (sec). Leaf size: 6

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

\[ y(x)\to \text {Indeterminate} \]

✗ Sympy

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

Timed Out