73.8.20 problem 13.4 (a)

Internal problem ID [15157]
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 : 13.4 (a)
Date solved : Monday, March 31, 2025 at 01:29:34 PM
CAS classification : [[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]

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

With initial conditions

\begin{align*} y \left (0\right )&=5\\ y^{\prime }\left (0\right )&=15 \end{align*}

✓ Maple. Time used: 0.094 (sec). Leaf size: 10

ode:=y(x)*diff(diff(y(x),x),x) = diff(y(x),x)^2; 
ic:=y(0) = 5, D(y)(0) = 15; 
dsolve([ode,ic],y(x), singsol=all);
 

\[ y = 5 \,{\mathrm e}^{3 x} \]

✓ Mathematica. Time used: 0.105 (sec). Leaf size: 12

ode=y[x]*D[y[x],{x,2}]==D[y[x],x]^2; 
ic={y[0]==5,Derivative[1][y][0] ==15}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to 5 e^{3 x} \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(y(x)*Derivative(y(x), (x, 2)) - Derivative(y(x), x)**2,0) 
ics = {y(0): 5, Subs(Derivative(y(x), x), x, 0): 15} 
dsolve(ode,func=y(x),ics=ics)
 

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