72.5.23 problem 10

Internal problem ID [14709]
Book : DIFFERENTIAL EQUATIONS by Paul Blanchard, Robert L. Devaney, Glen R. Hall. 4th edition. Brooks/Cole. Boston, USA. 2012
Section : Chapter 1. First-Order Differential Equations. Exercises section 1.6 page 89
Problem number : 10
Date solved : Tuesday, January 28, 2025 at 07:12:15 AM
CAS classification : [_quadrature]

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

✓ Solution by Maple

Time used: 0.039 (sec). Leaf size: 9

dsolve(diff(y(t),t)=tan( y(t)),y(t), singsol=all)
 

\[ y = \arcsin \left (c_{1} {\mathrm e}^{t}\right ) \]

✓ Solution by Mathematica

Time used: 35.180 (sec). Leaf size: 17

DSolve[D[y[t],t]==Tan[y[t]],y[t],t,IncludeSingularSolutions -> True]
 

\begin{align*} y(t)\to \arcsin \left (e^{t+c_1}\right ) \\ y(t)\to 0 \\ \end{align*}