30.3.27 problem 30

Internal problem ID [7483]
Book : Fundamentals of Differential Equations. By Nagle, Saff and Snider. 9th edition. Boston. Pearson 2018.
Section : Chapter 2, First order differential equations. Section 2.4, Exact equations. Exercises. page 64
Problem number : 30
Date solved : Sunday, October 12, 2025 at 01:34:31 AM
CAS classification : [_rational, [_Abel, `2nd type`, `class B`]]

\begin{align*} 5 x^{2} y+6 x^{3} y^{2}+4 x y^{2}+\left (2 x^{3}+3 x^{4} y+3 x^{2} y\right ) y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 891

ode:=5*x^2*y(x)+6*x^3*y(x)^2+4*x*y(x)^2+(2*x^3+3*x^4*y(x)+3*x^2*y(x))*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 67.024 (sec). Leaf size: 651

ode=( 5*x^2*y[x] + 6*x^3*y[x]^2 + 4*x*y[x]^2)+( 2*x^3+3*x^4*y[x] + 3*x^2*y[x] )*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to -\frac {x}{3 \left (x^2+1\right )}+\frac {\sqrt [3]{2} x^2}{3 \left (x^2+1\right ) \sqrt [3]{\frac {-2 x^7+27 e^{c_1} \left (x^2+1\right )^2+3 \sqrt {3} x^4 \sqrt {\frac {e^{c_1} \left (x^2+1\right )^2 \left (-4 x^7+27 e^{c_1} \left (x^2+1\right )^2\right )}{x^8}}}{x^4}}}+\frac {\sqrt [3]{\frac {-2 x^7+27 e^{c_1} \left (x^2+1\right )^2+3 \sqrt {3} x^4 \sqrt {\frac {e^{c_1} \left (x^2+1\right )^2 \left (-4 x^7+27 e^{c_1} \left (x^2+1\right )^2\right )}{x^8}}}{x^4}}}{3 \sqrt [3]{2} \left (x^2+1\right )}\\ y(x)&\to -\frac {x}{3 \left (x^2+1\right )}-\frac {i \left (\sqrt {3}-i\right ) x^2}{3\ 2^{2/3} \left (x^2+1\right ) \sqrt [3]{\frac {-2 x^7+27 e^{c_1} \left (x^2+1\right )^2+3 \sqrt {3} x^4 \sqrt {\frac {e^{c_1} \left (x^2+1\right )^2 \left (-4 x^7+27 e^{c_1} \left (x^2+1\right )^2\right )}{x^8}}}{x^4}}}+\frac {i \left (\sqrt {3}+i\right ) \sqrt [3]{\frac {-2 x^7+27 e^{c_1} \left (x^2+1\right )^2+3 \sqrt {3} x^4 \sqrt {\frac {e^{c_1} \left (x^2+1\right )^2 \left (-4 x^7+27 e^{c_1} \left (x^2+1\right )^2\right )}{x^8}}}{x^4}}}{6 \sqrt [3]{2} \left (x^2+1\right )}\\ y(x)&\to -\frac {x}{3 \left (x^2+1\right )}+\frac {i \left (\sqrt {3}+i\right ) x^2}{3\ 2^{2/3} \left (x^2+1\right ) \sqrt [3]{\frac {-2 x^7+27 e^{c_1} \left (x^2+1\right )^2+3 \sqrt {3} x^4 \sqrt {\frac {e^{c_1} \left (x^2+1\right )^2 \left (-4 x^7+27 e^{c_1} \left (x^2+1\right )^2\right )}{x^8}}}{x^4}}}-\frac {i \left (\sqrt {3}-i\right ) \sqrt [3]{\frac {-2 x^7+27 e^{c_1} \left (x^2+1\right )^2+3 \sqrt {3} x^4 \sqrt {\frac {e^{c_1} \left (x^2+1\right )^2 \left (-4 x^7+27 e^{c_1} \left (x^2+1\right )^2\right )}{x^8}}}{x^4}}}{6 \sqrt [3]{2} \left (x^2+1\right )} \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(6*x**3*y(x)**2 + 5*x**2*y(x) + 4*x*y(x)**2 + (3*x**4*y(x) + 2*x**3 + 3*x**2*y(x))*Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out