15.18.30 problem 30

Internal problem ID [3273]
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 : 30
Date solved : Sunday, March 30, 2025 at 01:26:05 AM
CAS classification : [[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]

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

With initial conditions

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

✓ Maple. Time used: 0.111 (sec). Leaf size: 15

ode:=2*diff(diff(y(x),x),x) = exp(y(x)); 
ic:=y(0) = 0, D(y)(0) = 1; 
dsolve([ode,ic],y(x), singsol=all);
 

\[ y = 2 \ln \left (2\right )+\ln \left (\frac {1}{\left (x -2\right )^{2}}\right ) \]

✓ Mathematica. Time used: 0.049 (sec). Leaf size: 15

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

\[ y(x)\to -2 \log \left (1-\frac {x}{2}\right ) \]

✗ Sympy

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