15.18.20 problem 20

Internal problem ID [3263]
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 : 20
Date solved : Sunday, March 30, 2025 at 01:25:36 AM
CAS classification : [[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_xy]]

\begin{align*} y^{\prime \prime }+2 {y^{\prime }}^{2}&=0 \end{align*}

✓ Maple. Time used: 0.017 (sec). Leaf size: 17

ode:=diff(diff(y(x),x),x)+2*diff(y(x),x)^2 = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {\ln \left (2\right )}{2}+\frac {\ln \left (c_1 x +c_2 \right )}{2} \]

✓ Mathematica. Time used: 0.208 (sec). Leaf size: 21

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

\[ y(x)\to \frac {1}{2} \log (2 x-c_1)+c_2 \]

✓ Sympy. Time used: 0.550 (sec). Leaf size: 12

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

\[ y{\left (x \right )} = C_{1} + \frac {\log {\left (C_{2} + 2 x \right )}}{2} \]