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 : Sunday, March 30, 2025 at 12:23:38 PM
CAS classification : system_of_ODEs

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

✗ Maple

ode:=[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)]; 
dsolve(ode);
 

\[ \text {No solution found} \]

✗ Mathematica

ode={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]}; 
ic={}; 
DSolve[{ode,ic},{y1[x],y2[x],y3[x]},x,IncludeSingularSolutions->True]
 

Not solved

✗ Sympy

from sympy import * 
x = symbols("x") 
y__1 = Function("y__1") 
y__2 = Function("y__2") 
y__3 = Function("y__3") 
ode=[Eq(-x*y__3(x) - 3*y__1(x) + Derivative(y__1(x), x),0),Eq(-x**3*y__3(x) - y__2(x) + Derivative(y__2(x), x),0),Eq(-2*x*y__1(x) + y__2(x) - y__3(x)*exp(x) + Derivative(y__3(x), x),0)] 
ics = {} 
dsolve(ode,func=[y__1(x),y__2(x),y__3(x)],ics=ics)
 

NotImplementedError :