85.18.4 problem 1 (d)

Internal problem ID [22550]
Book : Applied Differential Equations. By Murray R. Spiegel. 3rd edition. 1980. Pearson. ISBN 978-0130400970
Section : Chapter two. First order and simple higher order ordinary differential equations. A Exercises at page 52
Problem number : 1 (d)
Date solved : Thursday, October 02, 2025 at 08:50:23 PM
CAS classification : [[_1st_order, `_with_symmetry_[F(x)*G(y),0]`]]

\begin{align*} \left (x +x^{3} \sin \left (2 y\right )\right ) y^{\prime }-2 y&=0 \end{align*}

✓ Maple. Time used: 0.010 (sec). Leaf size: 22

ode:=(x+x^3*sin(2*y(x)))*diff(y(x),x)-2*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {\operatorname {RootOf}\left (\textit {\_Z} +2 c_1 \,x^{2}-\cos \left (\textit {\_Z} \right ) x^{2}\right )}{2} \]

✓ Mathematica. Time used: 0.103 (sec). Leaf size: 22

ode=(x+x^3*Sin[2*y[x]] )*D[y[x],x]-2*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ \text {Solve}\left [\frac {y(x)}{x^2}-\frac {1}{2} \cos (2 y(x))=c_1,y(x)\right ] \]

✓ Sympy. Time used: 2.007 (sec). Leaf size: 19

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((x**3*sin(2*y(x)) + x)*Derivative(y(x), x) - 2*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ C_{1} + \frac {\cos {\left (2 y{\left (x \right )} \right )}}{4} - \frac {y{\left (x \right )}}{2 x^{2}} = 0 \]