15.8.13 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 : Monday, January 27, 2025 at 07:08:44 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.011 (sec). Leaf size: 14

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

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

✓ Solution by Mathematica

Time used: 16.467 (sec). Leaf size: 25

DSolve[Tan[y[x]]==(3*x+4)*D[y[x],x],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*}