49.25.1 problem 2

Internal problem ID [7772]
Book : An introduction to Ordinary Differential Equations. Earl A. Coddington. Dover. NY 1961
Section : Chapter 6. Existence and uniqueness of solutions to systems and nth order equations. Page 254
Problem number : 2
Date solved : Monday, January 27, 2025 at 03:21:39 PM
CAS classification : system_of_ODEs

\begin{align*} y_{1}^{\prime }\left (x \right )&=3 y_{1} \left (x \right )+x y_{3} \left (x \right )\\ y_{2}^{\prime }\left (x \right )&=y_{2} \left (x \right )+x^{3} y_{3} \left (x \right )\\ y_{3}^{\prime }\left (x \right )&=2 y_{1} \left (x \right ) x -y_{2} \left (x \right )+{\mathrm e}^{x} y_{3} \left (x \right ) \end{align*}

✗ Solution by Maple

dsolve([diff(y__1(x),x)=3*y__1(x)+x*y__3(x),diff(y__2(x),x)=y__2(x)+x^3*y__3(x),diff(y__3(x),x)=2*x*y__1(x)-y__2(x)+exp(x)*y__3(x)],singsol=all)
 

\[ \text {No solution found} \]

✗ Solution by Mathematica

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

DSolve[{D[ y1[x],x]==3*y1[x]+x*y3[x],D[ y2[x],x]==y2[x]+x^3*y3[x],D[ y3[x],x]==2*x*y1[x]-y2[x]+Exp[x]*y3[x]},{y1[x],y2[x],y3[x]},x,IncludeSingularSolutions -> True]
 

Not solved