71.17.7 problem 13 (b(i))

Internal problem ID [14563]
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 : Tuesday, January 28, 2025 at 06:43:30 AM
CAS classification : system_of_ODEs

\begin{align*} y_{1}^{\prime }\left (x \right )&=\sin \left (x \right ) y_{1} \left (x \right )+\sqrt {x}\, y_{2} \left (x \right )+\ln \left (x \right )\\ y_{2}^{\prime }\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*}

✗ Solution by Maple

dsolve([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, y__1(1) = 1, y__2(1) = -1], singsol=all)
 

\[ \text {No solution found} \]

✗ Solution by Mathematica

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

DSolve[{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},{y1[1]==1,y2[1]==-1},{y1[x],y2[x]},x,IncludeSingularSolutions -> True]
 

Not solved