Internal problem ID [12526]
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 c.
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*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 44
dsolve([diff(y__1(x),x)=5/x*y__1(x)+4/x*y__2(x)-2*x,diff(y__2(x),x)=-6/x*y__1(x)-5/x*y__2(x)+5*x],[y__1(x), y__2(x)], singsol=all)
\[ y_{1} \left (x \right ) = -\frac {3 c_{1} x^{2}-6 x^{3}+2 c_{2}}{3 x} \] \[ y_{2} \left (x \right ) = \frac {c_{1} x^{2}-x^{3}+c_{2}}{x} \]
✓ Solution by Mathematica
Time used: 0.013 (sec). Leaf size: 44
DSolve[{y1'[x]==5/x*y1[x]+4/x*y2[x]-2*x,y2'[x]==-6/x*y1[x]-5/x*y2[x]+5*x},{y1[x],y2[x]},x,IncludeSingularSolutions -> True]
\begin{align*} \text {y1}(x)\to 2 x^2+c_2 x+\frac {c_1}{x} \text {y2}(x)\to -x^2-c_2 x-\frac {3 c_1}{2 x} \end{align*}