74.4.11 problem 11

Internal problem ID [15904]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 2. First Order Equations. Exercises 2.2, page 39
Problem number : 11
Date solved : Tuesday, January 28, 2025 at 08:18:10 AM
CAS classification : [_separable]

\begin{align*} 3 \sin \left (x \right )-4 \cos \left (y\right ) y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 13

dsolve(3*sin(x)-4*cos(y(x))*diff(y(x),x)=0,y(x), singsol=all)
 

\[ y = \arcsin \left (-\frac {3 \cos \left (x \right )}{4}+\frac {3 c_{1}}{4}\right ) \]

✓ Solution by Mathematica

Time used: 0.232 (sec). Leaf size: 35

DSolve[3*Sin[x]-4*Cos[y[x]]*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}\cos (K[1])dK[1]\&\right ]\left [\int _1^x\frac {3}{4} \sin (K[2])dK[2]+c_1\right ] \]