Internal problem ID [12827]
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)).
ODE order: 1.
ODE degree: 1.
Solve \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 \[ [y_{1} \left (1\right ) = 1, y_{2} \left (1\right ) = -1] \]
✗ 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: 0.0 (sec). Leaf size: 0
DSolve[{y1'[x]==Sin[x]*y1[x]+Sqrt[x]*y2[x]+Log[x],y2'[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