72.1.11 problem 1 (L)

Internal problem ID [19352]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 1. The Nature of Differential Equations. Separable Equations. Section 2. Problems at page 9
Problem number : 1 (L)
Date solved : Thursday, October 02, 2025 at 04:19:23 PM
CAS classification : [[_homogeneous, `class G`], _rational]

\begin{align*} x y^{\prime }+y&=x^{4} {y^{\prime }}^{2} \end{align*}

✓ Maple. Time used: 0.178 (sec). Leaf size: 81

ode:=x*diff(y(x),x)+y(x) = x^4*diff(y(x),x)^2; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= -\frac {1}{4 x^{2}} \\ y &= \frac {i c_1 -x}{x \,c_1^{2}} \\ y &= \frac {i c_1 -x}{x \,c_1^{2}} \\ y &= \frac {-i c_1 -x}{x \,c_1^{2}} \\ y &= \frac {-i c_1 -x}{x \,c_1^{2}} \\ \end{align*}

✓ Mathematica. Time used: 0.315 (sec). Leaf size: 123

ode=y[x]+x*D[y[x],x]==x^4*D[y[x],x]^2; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} \text {Solve}\left [-\frac {x \sqrt {4 x^2 y(x)+1} \text {arctanh}\left (\sqrt {4 x^2 y(x)+1}\right )}{\sqrt {4 x^4 y(x)+x^2}}-\frac {1}{2} \log (y(x))=c_1,y(x)\right ]\\ \text {Solve}\left [\frac {x \sqrt {4 x^2 y(x)+1} \text {arctanh}\left (\sqrt {4 x^2 y(x)+1}\right )}{\sqrt {4 x^4 y(x)+x^2}}-\frac {1}{2} \log (y(x))=c_1,y(x)\right ]\\ y(x)&\to 0 \end{align*}

✓ Sympy. Time used: 2.533 (sec). Leaf size: 10

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x**4*Derivative(y(x), x)**2 + x*Derivative(y(x), x) + y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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