69.16.52 problem 525

Internal problem ID [18312]
Book : A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV, G.I. MARKARENKO. MIR, MOSCOW. 1983
Section : Chapter 2 (Higher order ODEs). Section 15.3 Nonhomogeneous linear equations with constant coefficients. Trial and error method. Exercises page 132
Problem number : 525
Date solved : Thursday, October 02, 2025 at 03:10:20 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+5 y^{\prime }+6 y&=10 \left (1-x \right ) {\mathrm e}^{-2 x} \end{align*}

✓ Maple. Time used: 0.005 (sec). Leaf size: 26

ode:=diff(diff(y(x),x),x)+5*diff(y(x),x)+6*y(x) = 10*(1-x)*exp(-2*x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \left (-5 x^{2}+c_2 +20 x \right ) {\mathrm e}^{-2 x}+{\mathrm e}^{-3 x} c_1 \]

✓ Mathematica. Time used: 0.02 (sec). Leaf size: 30

ode=D[y[x],{x,2}]+5*D[y[x],x]+6*y[x]==10*(1-x)*Exp[-2*x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to e^{-3 x} \left (e^x \left (-5 x^2+20 x-20+c_2\right )+c_1\right ) \end{align*}

✓ Sympy. Time used: 0.185 (sec). Leaf size: 22

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((10*x - 10)*exp(-2*x) + 6*y(x) + 5*Derivative(y(x), x) + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \left (C_{1} + C_{2} e^{- x} - 5 x^{2} + 20 x\right ) e^{- 2 x} \]