67.2.61 problem Problem 20(h)

Internal problem ID [13947]
Book : APPLIED DIFFERENTIAL EQUATIONS The Primary Course by Vladimir A. Dobrushkin. CRC Press 2015
Section : Chapter 4, Second and Higher Order Linear Differential Equations. Problems page 221
Problem number : Problem 20(h)
Date solved : Monday, March 31, 2025 at 08:20:02 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+\left (2 x +5\right ) y^{\prime }+\left (4 x +8\right ) y&={\mathrm e}^{-2 x} \end{align*}

✓ Maple. Time used: 0.005 (sec). Leaf size: 29

ode:=diff(diff(y(x),x),x)+(2*x+5)*diff(y(x),x)+(4*x+8)*y(x) = exp(-2*x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = {\mathrm e}^{-x \left (x +3\right )} \left (\operatorname {erf}\left (i \left (x +\frac {1}{2}\right )\right ) c_1 +c_2 \right )+\frac {{\mathrm e}^{-2 x}}{2} \]

✓ Mathematica. Time used: 0.319 (sec). Leaf size: 64

ode=D[y[x],{x,2}]+(2*x+5)*D[y[x],x]+(4*x+8)*y[x]==Exp[-2*x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((2*x + 5)*Derivative(y(x), x) + (4*x + 8)*y(x) + Derivative(y(x), (x, 2)) - exp(-2*x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : The given ODE Derivative(y(x), x) - (-4*x*y(x)*exp(2*x) - 8*y(x)*exp(2*x) - exp(2*x)*Derivative(y(x), (x, 2)) + 1)*exp(-2*x)/(2*x + 5) cannot be solved by the factorable group method