Internal problem ID [12823]
Internal file name [OUTPUT/11476_Saturday_November_04_2023_08_47_32_AM_68493840/index.tex]
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.
ODE order: 1.
ODE degree: 1.
The type(s) of ODE detected by this program : "system of linear ODEs" Unable to solve or complete the solution.
Solve \begin {align*} y_{1}^{\prime }\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}}\\ y_{2}^{\prime }\left (x \right )&=2 y_{1} \left (x \right )+1-6 x \end {align*}
With initial conditions \[ [y_{1} \left (1\right ) = -2, y_{2} \left (1\right ) = -5] \] Does not currently support non autonomous system of first order linear differential equations. The following is the phase plot
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 20
dsolve([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, y__1(1) = -2, y__2(1) = -5], singsol=all)
\begin{align*} y_{1} \left (x \right ) &= -2 x \\ y_{2} \left (x \right ) &= -1+x \left (-5 x +1\right ) \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.012 (sec). Leaf size: 19
DSolve[{y1'[x]==2*y1[x]/x-y2[x]/x^2-3+1/x-1/x^2,y2'[x]==2*y1[x]+1-6*x},{y1[1]==-2,y2[1]==-5},{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*}