71.17.4 problem 5

Internal problem ID [14489]
Book : Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section : Chapter 7. Systems of First-Order Differential Equations. Exercises page 329
Problem number : 5
Date solved : Monday, March 31, 2025 at 12:28:30 PM
CAS classification : system_of_ODEs

\begin{align*} \frac {d}{d x}y_{1} \left (x \right )&=\frac {2 y_{1} \left (x \right )}{x}-\frac {y_{2} \left (x \right )}{x^{2}}-3+\frac {1}{x}-\frac {1}{x^{2}}\\ \frac {d}{d x}y_{2} \left (x \right )&=2 y_{1} \left (x \right )+1-6 x \end{align*}

With initial conditions

\begin{align*} y_{1} \left (1\right ) = -2\\ y_{2} \left (1\right ) = -5 \end{align*}

✓ Maple. Time used: 0.126 (sec). Leaf size: 19

ode:=[diff(y__1(x),x) = 2*y__1(x)/x-y__2(x)/x^2-3+1/x-1/x^2, diff(y__2(x),x) = 2*y__1(x)+1-6*x]; 
ic:=y__1(1) = -2y__2(1) = -5; 
dsolve([ode,ic]);
 

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

✓ Mathematica. Time used: 0.008 (sec). Leaf size: 19

ode={D[ y1[x],x]==2*y1[x]/x-y2[x]/x^2-3+1/x-1/x^2,D[ y2[x],x]==2*y1[x]+1-6*x}; 
ic={y1[1]==-2,y2[1]==-5}; 
DSolve[{ode,ic},{y1[x],y2[x]},x,IncludeSingularSolutions->True]
 

\begin{align*} \text {y1}(x)\to -2 x \\ \text {y2}(x)\to -5 x^2+x-1 \\ \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y__1 = Function("y__1") 
y__2 = Function("y__2") 
ode=[Eq(Derivative(y__1(x), x) + 3 - 2*y__1(x)/x - 1/x + y__2(x)/x**2 + x**(-2),0),Eq(6*x - 2*y__1(x) + Derivative(y__2(x), x) - 1,0)] 
ics = {} 
dsolve(ode,func=[y__1(x),y__2(x)],ics=ics)
 

NotImplementedError :