71.17.9 problem 13 (c(i))

Internal problem ID [14565]
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(i))
Date solved : Tuesday, January 28, 2025 at 06:43:31 AM
CAS classification : system_of_ODEs

\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 )}{\left (x -2\right )^{2}} \end{align*}

With initial conditions

\begin{align*} y_{1} \left (0\right ) = 0\\ y_{2} \left (0\right ) = 1 \end{align*}

✗ 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)/(x-2)^2, y__1(0) = 0, y__2(0) = 1], singsol=all)
 

\[ \text {No solution found} \]

✗ Solution by Mathematica

Time used: 0.000 (sec). Leaf size: 0

DSolve[{D[ y1[x],x]==Exp[-x]*y1[x]-Sqrt[x+1]*y2[x]+x^2,D[ y2[x],x]==y1[x]/(x-2)^2},{y1[0]==0,y2[0]==1},{y1[x],y2[x]},x,IncludeSingularSolutions -> True]
 

Not solved