73.6.11 problem 7.5 (a)

Internal problem ID [15071]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 7. The exact form and general integrating fators. Additional exercises. page 141
Problem number : 7.5 (a)
Date solved : Thursday, March 13, 2025 at 05:36:06 AM
CAS classification : [_separable]

\begin{align*} 1+y^{4}+x y^{3} y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 68

ode:=1+y(x)^4+x*y(x)^3*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= \frac {\left (-x^{4}+c_{1} \right )^{{1}/{4}}}{x} \\ y &= -\frac {\left (-x^{4}+c_{1} \right )^{{1}/{4}}}{x} \\ y &= -\frac {i \left (-x^{4}+c_{1} \right )^{{1}/{4}}}{x} \\ y &= \frac {i \left (-x^{4}+c_{1} \right )^{{1}/{4}}}{x} \\ \end{align*}

✓ Mathematica. Time used: 0.308 (sec). Leaf size: 218

ode=1+y[x]^4+x*y[x]^3*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)\to -\frac {\sqrt [4]{-x^4+e^{4 c_1}}}{x} \\ y(x)\to -\frac {i \sqrt [4]{-x^4+e^{4 c_1}}}{x} \\ y(x)\to \frac {i \sqrt [4]{-x^4+e^{4 c_1}}}{x} \\ y(x)\to \frac {\sqrt [4]{-x^4+e^{4 c_1}}}{x} \\ y(x)\to -\sqrt [4]{-1} \\ y(x)\to \sqrt [4]{-1} \\ y(x)\to -(-1)^{3/4} \\ y(x)\to (-1)^{3/4} \\ y(x)\to \frac {i x^3}{\left (-x^4\right )^{3/4}} \\ y(x)\to \frac {x^3}{\left (-x^4\right )^{3/4}} \\ y(x)\to \frac {i \sqrt [4]{-x^4}}{x} \\ y(x)\to \frac {\sqrt [4]{-x^4}}{x} \\ \end{align*}

✓ Sympy. Time used: 1.646 (sec). Leaf size: 65

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x*y(x)**3*Derivative(y(x), x) + y(x)**4 + 1,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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