71.17.5 problem 6

Internal problem ID [14561]
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 : 6
Date solved : Tuesday, January 28, 2025 at 08:25:30 PM
CAS classification : system_of_ODEs

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

With initial conditions

\begin{align*} y_{1} \left (-1\right ) = 3\\ y_{2} \left (-1\right ) = -3 \end{align*}

✓ Solution by Maple

Time used: 0.055 (sec). Leaf size: 38

dsolve([diff(y__1(x),x) = 5*y__1(x)/x+4*y__2(x)/x-2*x, diff(y__2(x),x) = -6*y__1(x)/x-5*y__2(x)/x+5*x, y__1(-1) = 3, y__2(-1) = -3], singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.020 (sec). Leaf size: 33

DSolve[{D[ y1[x],x]==5*y1[x]/x+4*y2[x]/x-2*x,D[ y2[x],x]==-6*y1[x]/x-5*y2[x]/x+5*x},{y1[-1]==3,y2[-1]==-3},{y1[x],y2[x]},x,IncludeSingularSolutions -> True]
 

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