Internal problem ID [12825]
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.
ODE order: 1.
ODE degree: 1.
Solve \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 \[ [y_{1} \left (-1\right ) = 3, y_{2} \left (-1\right ) = -3] \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 39
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: 0.021 (sec). Leaf size: 33
DSolve[{y1'[x]==5*y1[x]/x+4*y2[x]/x-2*x,y2'[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*}