35.7.3 problem 1 (c)

Internal problem ID [6185]
Book : Mathematical Methods in the Physical Sciences. third edition. Mary L. Boas. John Wiley. 2006
Section : Chapter 8, Ordinary differential equations. Section 7. Other second-Order equations. page 435
Problem number : 1 (c)
Date solved : Wednesday, March 05, 2025 at 12:23:57 AM
CAS classification : [[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Lagerstrom, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]

\begin{align*} y^{\prime \prime }+y y^{\prime }&=0 \end{align*}

With initial conditions

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

✓ Maple. Time used: 0.056 (sec). Leaf size: 12

ode:=diff(diff(y(x),x),x)+y(x)*diff(y(x),x) = 0; 
ic:=y(0) = 1, D(y)(0) = -1; 
dsolve([ode,ic],y(x), singsol=all);
 

\[ y = \cot \left (\frac {x}{2}+\frac {\pi }{4}\right ) \]

✗ Mathematica

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

{}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(y(x)*Derivative(y(x), x) + 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)
 

NotImplementedError : The given ODE Derivative(y(x), x) + Derivative(y(x), (x, 2))/y(x) cannot be solved by the factorable group method