Internal problem ID [2606]
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')`]
\[ \boxed {y^{\prime }-\frac {{\mathrm e}^{x}-\sin \left (y\right )}{x \cos \left (y\right )}=0} \]
✓ Solution by Maple
Time used: 0.0 (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: 11.572 (sec). Leaf size: 16
DSolve[y'[x]==(Exp[x]-Sin[y[x]])/(x*Cos[y[x]]),y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \arcsin \left (\frac {e^x+c_1}{x}\right ) \]