15.2.19 problem 19

Internal problem ID [2889]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 6, page 25
Problem number : 19
Date solved : Tuesday, March 04, 2025 at 03:00:52 PM
CAS classification : [[_homogeneous, `class A`], _dAlembert]

\begin{align*} y^{\prime }&=\frac {y}{x}+\tan \left (\frac {y}{x}\right ) \end{align*}

With initial conditions

\begin{align*} y \left (6\right )&=\pi \end{align*}

✓ Maple. Time used: 0.134 (sec). Leaf size: 10

ode:=diff(y(x),x) = y(x)/x+tan(y(x)/x); 
ic:=y(6) = Pi; 
dsolve([ode,ic],y(x), singsol=all);
 

\[ y = \arcsin \left (\frac {x}{12}\right ) x \]

✓ Mathematica. Time used: 9.007 (sec). Leaf size: 13

ode=D[y[x],x]==y[x]/x+Tan[y[x]/x]; 
ic=y[6]==Pi; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to x \arcsin \left (\frac {x}{12}\right ) \]

✓ Sympy. Time used: 1.115 (sec). Leaf size: 8

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-tan(y(x)/x) + Derivative(y(x), x) - y(x)/x,0) 
ics = {y(6): pi} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = x \operatorname {asin}{\left (\frac {x}{12} \right )} \]