75.18.27 problem 616

Internal problem ID [17044]
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. Initial value problem. Exercises page 140
Problem number : 616
Date solved : Monday, March 31, 2025 at 03:39:05 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-5 y^{\prime }+6 y&=2 \,{\mathrm e}^{-2 x} \left (9 \sin \left (2 x \right )+4 \cos \left (2 x \right )\right ) \end{align*}

With initial conditions

\begin{align*} y \left (\infty \right )&=0 \end{align*}

✓ Maple. Time used: 0.180 (sec). Leaf size: 30

ode:=diff(diff(y(x),x),x)-5*diff(y(x),x)+6*y(x) = 2*exp(-2*x)*(9*sin(2*x)+4*cos(2*x)); 
ic:=y(infinity) = 0; 
dsolve([ode,ic],y(x), singsol=all);
 

\[ y = \frac {\left (145 c_2 \,{\mathrm e}^{4 x}+36 \sin \left (2 x \right )+113 \cos \left (2 x \right )\right ) {\mathrm e}^{-2 x}}{145} \]

✗ Mathematica

ode=D[y[x],{x,2}]-5*D[y[x],x]+6*y[x]==2*Exp[-2*x]*(9*Sin[2*x]+4*Cos[2*x]); 
ic={y[Infinity]==0}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Not solved

✓ Sympy. Time used: 0.464 (sec). Leaf size: 36

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((-18*sin(2*x) - 8*cos(2*x))*exp(-2*x) + 6*y(x) - 5*Derivative(y(x), x) + Derivative(y(x), (x, 2)),0) 
ics = {y(oo): 0} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{2} e^{3 x} - C_{2} e^{2 x} + \frac {\left (36 \sin {\left (2 x \right )} + 113 \cos {\left (2 x \right )}\right ) e^{- 2 x}}{145} \]