29.1.13 problem 12

Internal problem ID [4620]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 1
Problem number : 12
Date solved : Sunday, March 30, 2025 at 03:30:45 AM
CAS classification : [_linear]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 11

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

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

✓ Mathematica. Time used: 0.128 (sec). Leaf size: 14

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

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

✓ Sympy. Time used: 0.382 (sec). Leaf size: 10

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

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