65.17.9 problem 13 (c(i))

Internal problem ID [15852]
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 : Thursday, October 02, 2025 at 10:28:40 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*}

✗ Maple

ode:=[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]; 
ic:=[y__1(0) = 0, y__2(0) = 1]; 
dsolve([ode,op(ic)]);
 

\[ \text {No solution found} \]

✗ Mathematica

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

Not solved

✗ Sympy

from sympy import * 
x = symbols("x") 
y__1 = Function("y__1") 
y__2 = Function("y__2") 
ode=[Eq(-x**2 + sqrt(x + 1)*y__2(x) - y__1(x)*exp(-x) + Derivative(y__1(x), x),0),Eq(Derivative(y__2(x), x) - y__1(x)/(x - 2)**2,0)] 
ics = {} 
dsolve(ode,func=[y__1(x),y__2(x)],ics=ics)
 

NotImplementedError :