23.3.166 problem 168

Internal problem ID [5880]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Part II. Chapter 3. THE DIFFERENTIAL EQUATION IS LINEAR AND OF SECOND ORDER, page 311
Problem number : 168
Date solved : Tuesday, September 30, 2025 at 02:05:32 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} {\mathrm e}^{2 x} y-\left (1+2 \,{\mathrm e}^{x}\right ) y^{\prime }+y^{\prime \prime }&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 25

ode:=exp(2*x)*y(x)-(1+2*exp(x))*diff(y(x),x)+diff(diff(y(x),x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = {\mathrm e}^{\frac {x}{2}+{\mathrm e}^{x}} \left (c_1 \sinh \left (\frac {x}{2}\right )+c_2 \cosh \left (\frac {x}{2}\right )\right ) \]

✓ Mathematica. Time used: 0.02 (sec). Leaf size: 20

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

\begin{align*} y(x)&\to e^{e^x} \left (c_2 e^x+c_1\right ) \end{align*}

✗ Sympy

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

False