78.8.45 problem 45

Internal problem ID [18172]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 2. First order equations. Miscellaneous Problems for Chapter 2. Problems at page 99
Problem number : 45
Date solved : Monday, March 31, 2025 at 05:21:04 PM
CAS classification : [_exact, [_1st_order, `_with_symmetry_[F(x)*G(y),0]`]]

\begin{align*} \frac {\cos \left (y\right )}{x +3}-\left (\sin \left (y\right ) \ln \left (5 x +15\right )-\frac {1}{y}\right ) y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.082 (sec). Leaf size: 19

ode:=cos(y(x))/(x+3)-(sin(y(x))*ln(5*x+15)-1/y(x))*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ \ln \left (y\right )+c_1 +\cos \left (y\right ) \left (\ln \left (5\right )+\ln \left (x +3\right )\right ) = 0 \]

✓ Mathematica. Time used: 0.574 (sec). Leaf size: 24

ode=Cos[y[x]]/(x+3) - (Sin[y[x]]*Log[5*x+15] - 1/y[x] ) *D[y[x],x]== 0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ \text {Solve}[\log (y(x))+\log (x+3) \cos (y(x))+\log (5) \cos (y(x))=c_1,y(x)] \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((-log(5*x + 15)*sin(y(x)) + 1/y(x))*Derivative(y(x), x) + cos(y(x))/(x + 3),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

ZeroDivisionError : polynomial division