49.3.4 problem 1(d)

Internal problem ID [7604]
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)
Date solved : Sunday, March 30, 2025 at 12:16:45 PM
CAS classification : [_linear]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 12

ode:=diff(y(x),x)-tan(x)*y(x) = exp(sin(x)); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \left ({\mathrm e}^{\sin \left (x \right )}+c_1 \right ) \sec \left (x \right ) \]

✓ Mathematica. Time used: 0.158 (sec). Leaf size: 15

ode=D[y[x],x]-Tan[x]*y[x]==Exp[Sin[x]]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.733 (sec). Leaf size: 12

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-y(x)*tan(x) - exp(sin(x)) + Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {C_{1} + e^{\sin {\left (x \right )}}}{\cos {\left (x \right )}} \]