88.12.11 problem 13

Internal problem ID [24067]
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. Miscellaneous Exercises at page 55
Problem number : 13
Date solved : Sunday, October 12, 2025 at 05:55:24 AM
CAS classification : system_of_ODEs

\begin{align*} x \left (\frac {d}{d x}y \left (x \right )\right )&=y \left (x \right )\\ \frac {d}{d x}z \left (x \right )&=3 y \left (x \right )-x \end{align*}

✓ Maple. Time used: 0.026 (sec). Leaf size: 23

ode:=[x*diff(y(x),x) = y(x), diff(z(x),x) = 3*y(x)-x]; 
dsolve(ode);
 

\begin{align*} y \left (x \right ) &= c_2 x \\ z \left (x \right ) &= \frac {3}{2} c_2 \,x^{2}-\frac {1}{2} x^{2}+c_1 \\ \end{align*}

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 28

ode={x*D[y[x],x]==y[x],D[z[x],x]==3*y[x]-x}; 
ic={}; 
DSolve[{ode,ic},{y[x],z[x]},x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to c_1 x\\ z(x)&\to \frac {1}{2} (-1+3 c_1) x^2+c_2 \end{align*}

✓ Sympy. Time used: 0.058 (sec). Leaf size: 20

from sympy import * 
x = symbols("x") 
y = Function("y") 
z = Function("z") 
ode=[Eq(x*Derivative(y(x), x) - y(x),0),Eq(x - 3*y(x) + Derivative(z(x), x),0)] 
ics = {} 
dsolve(ode,func=[y(x),z(x)],ics=ics)
 

\[ \left [ y{\left (x \right )} = C_{1} x, \ z{\left (x \right )} = C_{2} + x^{2} \left (\frac {3 C_{1}}{2} - \frac {1}{2}\right )\right ] \]