9.8.13 problem 13

Internal problem ID [3016]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 12, page 46
Problem number : 13
Date solved : Tuesday, September 30, 2025 at 06:21:48 AM
CAS classification : [_separable]

\begin{align*} \tan \left (y\right )&=\left (3 x +4\right ) y^{\prime } \end{align*}

✓ Maple. Time used: 0.006 (sec). Leaf size: 14

ode:=tan(y(x)) = (3*x+4)*diff(y(x),x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \arcsin \left (\left (3 x +4\right )^{{1}/{3}} c_1 \right ) \]

✓ Mathematica. Time used: 15.671 (sec). Leaf size: 25

ode=Tan[y[x]]==(3*x+4)*D[y[x],x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \arcsin \left (e^{c_1} \sqrt [3]{3 x+4}\right )\\ y(x)&\to 0 \end{align*}

✓ Sympy. Time used: 0.267 (sec). Leaf size: 29

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((-3*x - 4)*Derivative(y(x), x) + tan(y(x)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ \left [ y{\left (x \right )} = \pi - \operatorname {asin}{\left (C_{1} \sqrt [3]{3 x + 4} \right )}, \ y{\left (x \right )} = \operatorname {asin}{\left (C_{1} \sqrt [3]{3 x + 4} \right )}\right ] \]