65.18.7 problem 6 a

Internal problem ID [15868]
Book : Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section : Chapter 8. Linear Systems of First-Order Differential Equations. Exercises 8.3 page 379
Problem number : 6 a
Date solved : Sunday, October 12, 2025 at 05:33:02 AM
CAS classification : system_of_ODEs

\begin{align*} \frac {d}{d x}y_{1} \left (x \right )&=\frac {5 y_{1} \left (x \right )}{x}+\frac {4 y_{2} \left (x \right )}{x}\\ \frac {d}{d x}y_{2} \left (x \right )&=-\frac {6 y_{1} \left (x \right )}{x}-\frac {5 y_{2} \left (x \right )}{x} \end{align*}

✓ Maple. Time used: 0.093 (sec). Leaf size: 33

ode:=[diff(y__1(x),x) = 5*y__1(x)/x+4*y__2(x)/x, diff(y__2(x),x) = -6*y__1(x)/x-5*y__2(x)/x]; 
dsolve(ode);
 

\begin{align*} y_{1} \left (x \right ) &= \frac {c_1 \,x^{2}+c_2}{x} \\ y_{2} \left (x \right ) &= -\frac {2 c_1 \,x^{2}+3 c_2}{2 x} \\ \end{align*}

✓ Mathematica. Time used: 0.006 (sec). Leaf size: 34

ode={D[ y1[x],x]==5/x*y1[x]+4/x*y2[x],D[ y2[x],x]==-6/x*y1[x]-5/x*y2[x]}; 
ic={}; 
DSolve[{ode,ic},{y1[x],y2[x]},x,IncludeSingularSolutions->True]
 

\begin{align*} \text {y1}(x)&\to \frac {c_1}{x}+c_2 x\\ \text {y2}(x)&\to -\frac {3 c_1}{2 x}-c_2 x \end{align*}

✓ Sympy. Time used: 0.066 (sec). Leaf size: 22

from sympy import * 
x = symbols("x") 
y__1 = Function("y__1") 
y__2 = Function("y__2") 
ode=[Eq(Derivative(y__1(x), x) - 5*y__1(x)/x - 4*y__2(x)/x,0),Eq(Derivative(y__2(x), x) + 6*y__1(x)/x + 5*y__2(x)/x,0)] 
ics = {} 
dsolve(ode,func=[y__1(x),y__2(x)],ics=ics)
 

\[ \left [ y^{1}{\left (x \right )} = - \frac {2 C_{1}}{3 x} - C_{2} x, \ y^{2}{\left (x \right )} = \frac {C_{1}}{x} + C_{2} x\right ] \]