40.4.13 problem 19 (o)

Internal problem ID [6653]
Book : Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres. McGraw Hill 1952
Section : Chapter 6. Equations of first order and first degree (Linear equations). Supplemetary problems. Page 39
Problem number : 19 (o)
Date solved : Sunday, March 30, 2025 at 11:13:48 AM
CAS classification : [_Bernoulli]

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

✓ Maple. Time used: 0.011 (sec). Leaf size: 54

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

\begin{align*} x &= \frac {\sqrt {\left (\cos \left (y \right )+y \sin \left (y \right )+c_1 \right ) y}}{\cos \left (y \right )+y \sin \left (y \right )+c_1} \\ x &= -\frac {\sqrt {\left (\cos \left (y \right )+y \sin \left (y \right )+c_1 \right ) y}}{\cos \left (y \right )+y \sin \left (y \right )+c_1} \\ \end{align*}

✓ Mathematica. Time used: 0.276 (sec). Leaf size: 53

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

\begin{align*} x(y)\to -\frac {\sqrt {y}}{\sqrt {y \sin (y)+\cos (y)+c_1}} \\ x(y)\to \frac {\sqrt {y}}{\sqrt {y \sin (y)+\cos (y)+c_1}} \\ x(y)\to 0 \\ \end{align*}

✓ Sympy. Time used: 1.774 (sec). Leaf size: 36

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

\[ \left [ x{\left (y \right )} = - \sqrt {\frac {y}{C_{1} + y \sin {\left (y \right )} + \cos {\left (y \right )}}}, \ x{\left (y \right )} = \sqrt {\frac {y}{C_{1} + y \sin {\left (y \right )} + \cos {\left (y \right )}}}\right ] \]