88.11.9 problem 10

Internal problem ID [24056]
Book : Elementary Differential Equations. By Lee Roy Wilcox and Herbert J. Curtis. 1961 first edition. International texbook company. Scranton, Penn. USA. CAT number 61-15976
Section : Chapter 2. Differential equations of first order. Exercise at page 54
Problem number : 10
Date solved : Thursday, October 02, 2025 at 09:55:17 PM
CAS classification : system_of_ODEs

\begin{align*} y^{\prime }&=f \left (x \right )+a y+b z \left (x \right )\\ z^{\prime }\left (x \right )&=g \left (x \right )+c y+d z \left (x \right ) \end{align*}

✓ Maple. Time used: 0.314 (sec). Leaf size: 1066

ode:=[diff(y(x),x) = f(x)+a*y(x)+b*z(x), diff(z(x),x) = g(x)+c*y(x)+d*z(x)]; 
dsolve(ode);
 

\begin{align*} \text {Solution too large to show}\end{align*}

✓ Mathematica. Time used: 0.335 (sec). Leaf size: 1656

ode={D[y[x],x]==f[x]+a*y[x]+b*z[x],D[z[x],x]==g[x]+c*y[x]+d*z[x]}; 
ic={}; 
DSolve[{ode,ic},{y[x],z[x]},x,IncludeSingularSolutions->True]
 

Too large to display

✓ Sympy. Time used: 76.203 (sec). Leaf size: 2762

from sympy import * 
x = symbols("x") 
a = symbols("a") 
b = symbols("b") 
c = symbols("c") 
d = symbols("d") 
y = Function("y") 
z = Function("z") 
f = Function("f") 
g = Function("g") 
ode=[Eq(-a*y(x) - b*z(x) - f(x) + Derivative(y(x), x),0),Eq(-c*y(x) - d*z(x) - g(x) + Derivative(z(x), x),0)] 
ics = {} 
dsolve(ode,func=[y(x),z(x)],ics=ics)
 

\[ \text {Solution too large to show} \]