34.4.17 problem 19 (s)

Internal problem ID [7944]
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 (s)
Date solved : Tuesday, September 30, 2025 at 05:11:05 PM
CAS classification : [[_homogeneous, `class G`], _rational, _Bernoulli]

\begin{align*} 2 x y^{5}-y+2 x y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.006 (sec). Leaf size: 137

ode:=2*x*y(x)^5-y(x)+2*x*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= \frac {3^{{1}/{4}} \sqrt {-\sqrt {4 x^{3}+3 c_1}\, x}}{\sqrt {4 x^{3}+3 c_1}} \\ y &= \frac {3^{{1}/{4}} \sqrt {\sqrt {4 x^{3}+3 c_1}\, x}}{\sqrt {4 x^{3}+3 c_1}} \\ y &= -\frac {3^{{1}/{4}} \sqrt {-\sqrt {4 x^{3}+3 c_1}\, x}}{\sqrt {4 x^{3}+3 c_1}} \\ y &= -\frac {3^{{1}/{4}} \sqrt {\sqrt {4 x^{3}+3 c_1}\, x}}{\sqrt {4 x^{3}+3 c_1}} \\ \end{align*}

✓ Mathematica. Time used: 0.139 (sec). Leaf size: 109

ode=(2*x*y[x]^5-y[x])+2*x*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to -\frac {\sqrt {x}}{\sqrt [4]{\frac {4 x^3}{3}+c_1}}\\ y(x)&\to -\frac {i \sqrt {x}}{\sqrt [4]{\frac {4 x^3}{3}+c_1}}\\ y(x)&\to \frac {i \sqrt {x}}{\sqrt [4]{\frac {4 x^3}{3}+c_1}}\\ y(x)&\to \frac {\sqrt {x}}{\sqrt [4]{\frac {4 x^3}{3}+c_1}}\\ y(x)&\to 0 \end{align*}

✓ Sympy. Time used: 1.418 (sec). Leaf size: 88

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(2*x*y(x)**5 + 2*x*Derivative(y(x), x) - y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ \left [ y{\left (x \right )} = - \sqrt [4]{3} \sqrt [4]{\frac {x^{2}}{C_{1} + 4 x^{3}}}, \ y{\left (x \right )} = \sqrt [4]{3} \sqrt [4]{\frac {x^{2}}{C_{1} + 4 x^{3}}}, \ y{\left (x \right )} = - \sqrt [4]{3} i \sqrt [4]{\frac {x^{2}}{C_{1} + 4 x^{3}}}, \ y{\left (x \right )} = \sqrt [4]{3} i \sqrt [4]{\frac {x^{2}}{C_{1} + 4 x^{3}}}\right ] \]