73.8.47 problem 13.8 (ii)

Internal problem ID [15184]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 13. Higher order equations: Extending first order concepts. Additional exercises page 259
Problem number : 13.8 (ii)
Date solved : Monday, March 31, 2025 at 01:30:28 PM
CAS classification : [[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]]

\begin{align*} y^{\prime \prime }&=-2 x {y^{\prime }}^{2} \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=3\\ y^{\prime }\left (0\right )&=0 \end{align*}

✓ Maple. Time used: 0.059 (sec). Leaf size: 5

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

\[ y = 3 \]

✓ Mathematica. Time used: 23.378 (sec). Leaf size: 6

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

\[ y(x)\to 3 \]

✗ Sympy

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

ValueError : Couldnt solve for initial conditions