19.3.4 problem 12

Internal problem ID [3547]
Book : Differential equations and linear algebra, Stephen W. Goode, second edition, 2000
Section : 1.8, page 68
Problem number : 12
Date solved : Tuesday, March 04, 2025 at 04:45:24 PM
CAS classification : [[_homogeneous, `class A`], _rational, _dAlembert]

\begin{align*} x y^{\prime }&=\sqrt {16 x^{2}-y^{2}}+y \end{align*}

✓ Maple. Time used: 0.007 (sec). Leaf size: 29

ode:=x*diff(y(x),x) = (16*x^2-y(x)^2)^(1/2)+y(x); 
dsolve(ode,y(x), singsol=all);
 

\[ -\arctan \left (\frac {y \left (x \right )}{\sqrt {16 x^{2}-y \left (x \right )^{2}}}\right )+\ln \left (x \right )-c_{1} = 0 \]

✓ Mathematica. Time used: 0.405 (sec). Leaf size: 18

ode=x*D[y[x],x]==Sqrt[16*x^2-y[x]^2]+y[x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to -4 x \cosh (i \log (x)+c_1) \]

✓ Sympy. Time used: 0.928 (sec). Leaf size: 14

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x*Derivative(y(x), x) - sqrt(16*x**2 - y(x)**2) - y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = - 4 x \sin {\left (C_{1} - \log {\left (x \right )} \right )} \]