Internal problem ID [5182]
Book: An introduction to Ordinary Differential Equations. Earl A. Coddington. Dover. NY
1961
Section: Chapter 1. Introduction– Linear equations of First Order. Page 45
Problem number: 1(d).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
\[ \boxed {y^{\prime }-y \tan \left (x \right )-{\mathrm e}^{\sin \left (x \right )}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 14
dsolve(diff(y(x),x)-tan(x)*y(x)=exp(sin(x)),y(x), singsol=all)
\[ y \left (x \right ) = \frac {{\mathrm e}^{\sin \left (x \right )}+c_{1}}{\cos \left (x \right )} \]
✓ Solution by Mathematica
Time used: 0.155 (sec). Leaf size: 15
DSolve[y'[x]-Tan[x]*y[x]==Exp[Sin[x]],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \sec (x) \left (e^{\sin (x)}+c_1\right ) \\ \end{align*}