74.8.2 problem 2

Internal problem ID [16138]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 2. First Order Equations. Review exercises, page 80
Problem number : 2
Date solved : Tuesday, January 28, 2025 at 08:51:42 AM
CAS classification : [_separable]

\begin{align*} \cos \left (4 x \right )-8 \sin \left (y\right ) y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 19

dsolve(cos(4*x)-8*sin(y(x))*diff(y(x),x)=0,y(x), singsol=all)
 

\[ y = \frac {\pi }{2}+\arcsin \left (\frac {\sin \left (4 x \right )}{32}+\frac {c_{1}}{8}\right ) \]

✓ Solution by Mathematica

Time used: 0.306 (sec). Leaf size: 37

DSolve[Cos[4*x]-8*Sin[y[x]]*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}\sin (K[1])dK[1]\&\right ]\left [\int _1^x\frac {1}{8} \cos (4 K[2])dK[2]+c_1\right ] \]