Internal problem ID [12829]
Internal file name [OUTPUT/11482_Saturday_November_04_2023_08_47_33_AM_94405046/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: 13 (c(ii)).
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 )&={\mathrm e}^{-x} y_{1} \left (x \right )-\sqrt {1+x}\, y_{2} \left (x \right )+x^{2}\\ y_{2}^{\prime }\left (x \right )&=\frac {y_{1} \left (x \right )}{x^{2}-4 x +4} \end {align*}
With initial conditions \[ [y_{1} \left (3\right ) = 1, y_{2} \left (3\right ) = 0] \] 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) = exp(-x)*y__1(x)-(1+x)^(1/2)*y__2(x)+x^2, diff(y__2(x),x) = y__1(x)/(-2+x)^2, y__1(3) = 1, y__2(3) = 0], singsol=all)
\[ \text {No solution found} \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[{y1'[x]==Exp[-x]*y1[x]-Sqrt[x+1]*y2[x]+x^2,y2'[x]==y1[x]/(x-2)^2},{y1[3]==1,y2[3]==0},{y1[x],y2[x]},x,IncludeSingularSolutions -> True]
Not solved