60.3.29 problem 1034

Internal problem ID [11025]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1034
Date solved : Sunday, March 30, 2025 at 07:39:33 PM
CAS classification : [[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]

\begin{align*} y^{\prime \prime }-y^{\prime }+{\mathrm e}^{2 x} y&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 15

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

\[ y = c_1 \sin \left ({\mathrm e}^{x}\right )+c_2 \cos \left ({\mathrm e}^{x}\right ) \]

✓ Mathematica. Time used: 0.023 (sec). Leaf size: 20

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

\[ y(x)\to c_1 \cos \left (e^x\right )+c_2 \sin \left (e^x\right ) \]

✗ Sympy

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

False