20.4.6 problem Problem 14

Internal problem ID [3641]
Book : Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition, 2015
Section : Chapter 1, First-Order Differential Equations. Section 1.8, Change of Variables. page 79
Problem number : Problem 14
Date solved : Sunday, March 30, 2025 at 01:57:30 AM
CAS classification : [[_homogeneous, `class A`], _rational, _dAlembert]

\begin{align*} x y^{\prime }-y&=\sqrt {9 x^{2}+y^{2}} \end{align*}

✓ Maple. Time used: 0.028 (sec). Leaf size: 28

ode:=x*diff(y(x),x)-y(x) = (9*x^2+y(x)^2)^(1/2); 
dsolve(ode,y(x), singsol=all);
 

\[ \frac {-c_1 \,x^{2}+\sqrt {9 x^{2}+y^{2}}+y}{x^{2}} = 0 \]

✓ Mathematica. Time used: 0.335 (sec). Leaf size: 27

ode=x*D[y[x],x]-y[x]==Sqrt[9*x^2+y[x]^2]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {1}{2} e^{-c_1} \left (-9+e^{2 c_1} x^2\right ) \]

✓ Sympy. Time used: 1.252 (sec). Leaf size: 14

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x*Derivative(y(x), x) - sqrt(9*x**2 + y(x)**2) - y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = - 3 x \sinh {\left (C_{1} - \log {\left (x \right )} \right )} \]