Internal problem ID [12841]
Internal file name [OUTPUT/11494_Monday_November_06_2023_01_31_03_PM_39604673/index.tex]
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: 4.
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 )&=2 y_{1} \left (x \right ) x -x^{2} y_{2} \left (x \right )+4 x\\ y_{2}^{\prime }\left (x \right )&=y_{1} \left (x \right ) {\mathrm e}^{x}+3 \,{\mathrm e}^{-x} y_{2} \left (x \right )-4 \cos \left (x \right )^{3}+3 \cos \left (x \right ) \end {align*}
Does not currently support non autonomous system of first order linear differential equations. The following is the phase plot
✗ Solution by Maple
dsolve([diff(y__1(x),x)=2*x*y__1(x)-x^2*y__2(x)+4*x,diff(y__2(x),x)=exp(x)*y__1(x)+3*exp(-x)*y__2(x)-cos(3*x)],singsol=all)
\[ \text {No solution found} \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[{y1'[x]==2*x*y1[x]-x^2*y2[x]+4*x,y2'[x]==Exp[x]*y1[x]+3*Exp[-x]*y2[x]-Cos[3*x]},{y1[x],y2[x]},x,IncludeSingularSolutions -> True]
Not solved