Internal problem ID [2097]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [y=_G(x,y')]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {{\mathrm e}^{x}-\sin \relax (y)}{x \cos \relax (y)}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.009 (sec). Leaf size: 15
dsolve(diff(y(x),x)=(exp(x)-sin(y(x)))/(x*cos(y(x))),y(x), singsol=all)
\[ y \relax (x ) = \arcsin \left (\frac {-c_{1}+{\mathrm e}^{x}}{x}\right ) \]
✓ Solution by Mathematica
Time used: 2.992 (sec). Leaf size: 16
DSolve[y'[x]==(Exp[x]-Sin[y[x]])/(x*Cos[y[x]]),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \text {ArcSin}\left (\frac {e^x+c_1}{x}\right ) \\ \end{align*}