85.15.17 problem 3 (b)

Internal problem ID [22542]
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 47
Problem number : 3 (b)
Date solved : Thursday, October 02, 2025 at 08:49:27 PM
CAS classification : [[_homogeneous, `class G`], _rational]

\begin{align*} y+\left (4 x -y^{2}\right ) y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.005 (sec). Leaf size: 970

ode:=y(x)+(4*x-y(x)^2)*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} \text {Solution too large to show}\end{align*}

✓ Mathematica. Time used: 60.072 (sec). Leaf size: 597

ode=y[x]+(4*x-y[x]^2)*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to -\sqrt {\sqrt [3]{8 x^3+\sqrt {9 c_1{}^2-48 c_1 x^3}-3 c_1}+\frac {4 x^2}{\sqrt [3]{8 x^3+\sqrt {9 c_1{}^2-48 c_1 x^3}-3 c_1}}+2 x}\\ y(x)&\to \sqrt {\sqrt [3]{8 x^3+\sqrt {9 c_1{}^2-48 c_1 x^3}-3 c_1}+\frac {4 x^2}{\sqrt [3]{8 x^3+\sqrt {9 c_1{}^2-48 c_1 x^3}-3 c_1}}+2 x}\\ y(x)&\to -\sqrt {\frac {1}{2} \left (-1-i \sqrt {3}\right ) \sqrt [3]{8 x^3+\sqrt {9 c_1{}^2-48 c_1 x^3}-3 c_1}+\frac {2 i \left (\sqrt {3}+i\right ) x^2}{\sqrt [3]{8 x^3+\sqrt {9 c_1{}^2-48 c_1 x^3}-3 c_1}}+2 x}\\ y(x)&\to \sqrt {\frac {1}{2} \left (-1-i \sqrt {3}\right ) \sqrt [3]{8 x^3+\sqrt {9 c_1{}^2-48 c_1 x^3}-3 c_1}+\frac {2 i \left (\sqrt {3}+i\right ) x^2}{\sqrt [3]{8 x^3+\sqrt {9 c_1{}^2-48 c_1 x^3}-3 c_1}}+2 x}\\ y(x)&\to -\sqrt {\frac {1}{2} i \left (\sqrt {3}+i\right ) \sqrt [3]{8 x^3+\sqrt {9 c_1{}^2-48 c_1 x^3}-3 c_1}-\frac {\left (2+2 i \sqrt {3}\right ) x^2}{\sqrt [3]{8 x^3+\sqrt {9 c_1{}^2-48 c_1 x^3}-3 c_1}}+2 x}\\ y(x)&\to \sqrt {\frac {1}{2} i \left (\sqrt {3}+i\right ) \sqrt [3]{8 x^3+\sqrt {9 c_1{}^2-48 c_1 x^3}-3 c_1}-\frac {\left (2+2 i \sqrt {3}\right ) x^2}{\sqrt [3]{8 x^3+\sqrt {9 c_1{}^2-48 c_1 x^3}-3 c_1}}+2 x} \end{align*}

✗ Sympy

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

Timed Out