60.3.58 problem 1063

Internal problem ID [11054]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1063
Date solved : Sunday, March 30, 2025 at 07:40:30 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-\left (2 \,{\mathrm e}^{x}+1\right ) y^{\prime }+{\mathrm e}^{2 x} y-{\mathrm e}^{3 x}&=0 \end{align*}

✓ Maple. Time used: 0.010 (sec). Leaf size: 28

ode:=diff(diff(y(x),x),x)-(2*exp(x)+1)*diff(y(x),x)+exp(2*x)*y(x)-exp(3*x) = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.075 (sec). Leaf size: 66

ode=-E^(3*x) + 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]
 

\[ y(x)\to e^{e^x} \left (\int _1^x-e^{3 K[1]-e^{K[1]}}dK[1]+e^x \int _1^xe^{2 K[2]-e^{K[2]}}dK[2]+c_2 e^x+c_1\right ) \]

✗ 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) - exp(3*x) + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : The given ODE Derivative(y(x), x) - (y(x)*exp(2*x) - exp(3*x) + Derivative(y(x), (x, 2)))/(2*exp(x) + 1) cannot be solved by the factorable group method