23.4.162 problem 162

Internal problem ID [6464]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Part II. Chapter 4. THE NONLINEAR EQUATION OF SECOND ORDER, page 380
Problem number : 162
Date solved : Tuesday, September 30, 2025 at 03:01:31 PM
CAS classification : [[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_y_y1]]

\begin{align*} y y^{\prime \prime }&={y^{\prime }}^{2} \left (1-\sin \left (y\right ) y^{\prime }-\cos \left (y\right ) y y^{\prime }\right ) \end{align*}

✓ Maple. Time used: 0.058 (sec). Leaf size: 24

ode:=y(x)*diff(diff(y(x),x),x) = diff(y(x),x)^2*(1-sin(y(x))*diff(y(x),x)-cos(y(x))*y(x)*diff(y(x),x)); 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= c_1 \\ -\cos \left (y\right )+c_1 \ln \left (y\right )-x -c_2 &= 0 \\ \end{align*}

✓ Mathematica. Time used: 0.289 (sec). Leaf size: 69

ode=y[x]*D[y[x],{x,2}] == D[y[x],x]^2*(1 - Sin[y[x]]*D[y[x],x] - Cos[y[x]]*y[x]*D[y[x],x]); 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \text {InverseFunction}[-\cos (\text {$\#$1})+c_1 \log (\text {$\#$1})\&][x+c_2]\\ y(x)&\to \text {InverseFunction}[-\cos (\text {$\#$1})-c_1 \log (\text {$\#$1})\&][x+c_2]\\ y(x)&\to \text {InverseFunction}[-\cos (\text {$\#$1})+c_1 \log (\text {$\#$1})\&][x+c_2] \end{align*}

✗ Sympy

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

Timed Out