71.17.7 problem 13 (b(i))

Internal problem ID [14492]
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 (b(i))
Date solved : Monday, March 31, 2025 at 12:28:33 PM
CAS classification : system_of_ODEs

\begin{align*} \frac {d}{d x}y_{1} \left (x \right )&=\sin \left (x \right ) y_{1} \left (x \right )+\sqrt {x}\, y_{2} \left (x \right )+\ln \left (x \right )\\ \frac {d}{d x}y_{2} \left (x \right )&=\tan \left (x \right ) y_{1} \left (x \right )-{\mathrm e}^{x} y_{2} \left (x \right )+1 \end{align*}

With initial conditions

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

✗ Maple

ode:=[diff(y__1(x),x) = sin(x)*y__1(x)+x^(1/2)*y__2(x)+ln(x), diff(y__2(x),x) = tan(x)*y__1(x)-exp(x)*y__2(x)+1]; 
ic:=y__1(1) = 1y__2(1) = -1; 
dsolve([ode,ic]);
 

\[ \text {No solution found} \]

✗ Mathematica

ode={D[ y1[x],x]==Sin[x]*y1[x]+Sqrt[x]*y2[x]+Log[x],D[ y2[x],x]==Tan[x]*y1[x]-Exp[x]*y2[x]+1}; 
ic={y1[1]==1,y2[1]==-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(-sqrt(x)*y__2(x) - y__1(x)*sin(x) - log(x) + Derivative(y__1(x), x),0),Eq(-y__1(x)*tan(x) + y__2(x)*exp(x) + Derivative(y__2(x), x) - 1,0)] 
ics = {} 
dsolve(ode,func=[y__1(x),y__2(x)],ics=ics)
 

NotImplementedError :