20.1.20 problem Problem 28

Internal problem ID [3577]
Book : Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition, 2015
Section : Chapter 1, First-Order Differential Equations. Section 1.2, Basic Ideas and Terminology. page 21
Problem number : Problem 28
Date solved : Monday, January 27, 2025 at 07:45:25 AM
CAS classification : [`y=_G(x,y')`]

\begin{align*} y^{\prime }&=\frac {{\mathrm e}^{x}-\sin \left (y\right )}{x \cos \left (y\right )} \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 15

dsolve(diff(y(x),x)=(exp(x)-sin(y(x)))/(x*cos(y(x))),y(x), singsol=all)
 

\[ y \left (x \right ) = \arcsin \left (\frac {-c_{1} +{\mathrm e}^{x}}{x}\right ) \]

✓ Solution by Mathematica

Time used: 11.044 (sec). Leaf size: 16

DSolve[D[y[x],x]==(Exp[x]-Sin[y[x]])/(x*Cos[y[x]]),y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \arcsin \left (\frac {e^x+c_1}{x}\right ) \]