89.27.2 problem 2

Internal problem ID [24884]
Book : A short course in Differential Equations. Earl D. Rainville. Second edition. 1958. Macmillan Publisher, NY. CAT 58-5010
Section : Chapter 13. Systems of equations. Exercises at page 200
Problem number : 2
Date solved : Thursday, October 02, 2025 at 10:49:04 PM
CAS classification : system_of_ODEs

\begin{align*} y^{\prime }-2 y-v^{\prime }\left (x \right )-v \left (x \right )&=6 \,{\mathrm e}^{3 x}\\ 2 y^{\prime }-3 y+v^{\prime }\left (x \right )-3 v \left (x \right )&=6 \,{\mathrm e}^{3 x} \end{align*}

✓ Maple. Time used: 0.053 (sec). Leaf size: 46

ode:=[diff(y(x),x)-2*y(x)-diff(v(x),x)-v(x) = 6*exp(3*x), 2*diff(y(x),x)-3*y(x)+diff(v(x),x)-3*v(x) = 6*exp(3*x)]; 
dsolve(ode);
 

\begin{align*} v \left (x \right ) &= {\mathrm e}^{x} c_2 +{\mathrm e}^{x} x c_1 -{\mathrm e}^{3 x} \\ y \left (x \right ) &= -2 \,{\mathrm e}^{x} c_2 -2 \,{\mathrm e}^{x} x c_1 -3 \,{\mathrm e}^{x} c_1 +2 \,{\mathrm e}^{3 x} \\ \end{align*}

✓ Mathematica. Time used: 0.282 (sec). Leaf size: 183

ode={D[y[x],x]-2*y[x]+2*D[v[x],x]-v[x]==6*Exp[3*x],2*D[y[x],x]-3*y[x]+D[v[x],x]-3*v[x]==6*Exp[3*x]}; 
ic={}; 
DSolve[{ode,ic},{y[x],v[x]},x,IncludeSingularSolutions->True]
 

\begin{align*} v(x)&\to \frac {1}{30} e^{\frac {1}{2} \left (x-\sqrt {5} x\right )} \left (24 e^{\frac {1}{2} \left (5+\sqrt {5}\right ) x}+\left (2 \sqrt {5} c_2-5 \left (\sqrt {5}-3\right ) c_1\right ) e^{\sqrt {5} x}+5 \left (3+\sqrt {5}\right ) c_1-2 \sqrt {5} c_2\right )\\ y(x)&\to \frac {1}{6} e^{\frac {1}{2} \left (x-\sqrt {5} x\right )} \left (12 e^{\frac {1}{2} \left (5+\sqrt {5}\right ) x}+\left (2 \sqrt {5} c_1+\left (3+\sqrt {5}\right ) c_2\right ) e^{\sqrt {5} x}-2 \sqrt {5} c_1-\left (\sqrt {5}-3\right ) c_2\right ) \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
v = Function("v") 
ode=[Eq(-v(x) - 2*y(x) - 6*exp(3*x) + 2*Derivative(v(x), x) + Derivative(y(x), x),0),Eq(-3*v(x) - 3*y(x) - 6*exp(3*x) + Derivative(v(x), x) + 2*Derivative(y(x), x),0)] 
ics = {} 
dsolve(ode,func=[y(x),v(x)],ics=ics)
 

Timed Out