23.4.10 problem 11(a)

Internal problem ID [4175]
Book : Theory and solutions of Ordinary Differential equations, Donald Greenspan, 1960
Section : Chapter 6. Linear systems. Exercises at page 110
Problem number : 11(a)
Date solved : Tuesday, March 04, 2025 at 05:54:55 PM
CAS classification : system_of_ODEs

\begin{align*} \frac {d}{d x}y_{1} \left (x \right )&=1\\ \frac {d}{d x}y_{2} \left (x \right )&=2 y_{1} \left (x \right ) \end{align*}

✓ Maple. Time used: 4.181 (sec). Leaf size: 19

ode:=[diff(y__1(x),x) = 1, diff(y__2(x),x) = 2*y__1(x)]; 
dsolve(ode);
 

\begin{align*} y_{1} \left (x \right ) &= c_{2} +x \\ y_{2} \left (x \right ) &= 2 c_{2} x +x^{2}+c_{1} \\ \end{align*}

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 23

ode={D[y1[x],x]==1,D[y2[x],x]==2*y1[x]}; 
ic={}; 
DSolve[{ode,ic},{y1[x],y2[x]},x,IncludeSingularSolutions->True]
 

\begin{align*} \text {y1}(x)\to x+c_1 \\ \text {y2}(x)\to x^2+2 c_1 x+c_2 \\ \end{align*}

✓ Sympy. Time used: 0.070 (sec). Leaf size: 19

from sympy import * 
x = symbols("x") 
y__1 = Function("y__1") 
y__2 = Function("y__2") 
ode=[Eq(Derivative(y__1(x), x) - 1,0),Eq(-2*y__1(x) + Derivative(y__2(x), x),0)] 
ics = {} 
dsolve(ode,func=[y__1(x),y__2(x)],ics=ics)
 

\[ \left [ y^{1}{\left (x \right )} = C_{1} + x, \ y^{2}{\left (x \right )} = 2 C_{1} x + 2 C_{2} + x^{2}\right ] \]