88.5.6 problem 6

Internal problem ID [23980]
Book : Elementary Differential Equations. By Lee Roy Wilcox and Herbert J. Curtis. 1961 first edition. International texbook company. Scranton, Penn. USA. CAT number 61-15976
Section : Chapter 2. Differential equations of first order. Exercise at page 35
Problem number : 6
Date solved : Thursday, October 02, 2025 at 09:48:41 PM
CAS classification : [[_homogeneous, `class A`], _rational, _dAlembert]

\begin{align*} x \left (6 x^{2}+14 y^{2}\right )+y \left (13 x^{2}+30 y^{2}\right ) y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.155 (sec). Leaf size: 809

ode:=x*(6*x^2+14*y(x)^2)+y(x)*(13*x^2+30*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: 60.161 (sec). Leaf size: 754

ode=x*( 6*x^2+14*y[x]^2 ) + y[x]*( 13*x^2+30*y[x]^2 )*D[y[x],{x,1}]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to -\frac {\sqrt {\sqrt [3]{x^6+15 \sqrt {6 e^{2 c_1} x^6+2025 e^{4 c_1}}+675 e^{2 c_1}}-14 x^2+\frac {x^4}{\sqrt [3]{x^6+15 \sqrt {6 e^{2 c_1} x^6+2025 e^{4 c_1}}+675 e^{2 c_1}}}}}{\sqrt {30}}\\ y(x)&\to \frac {\sqrt {\sqrt [3]{x^6+15 \sqrt {6 e^{2 c_1} x^6+2025 e^{4 c_1}}+675 e^{2 c_1}}-14 x^2+\frac {x^4}{\sqrt [3]{x^6+15 \sqrt {6 e^{2 c_1} x^6+2025 e^{4 c_1}}+675 e^{2 c_1}}}}}{\sqrt {30}}\\ y(x)&\to -\sqrt {\frac {1}{60} \left (-1-i \sqrt {3}\right ) \sqrt [3]{x^6+15 \sqrt {6 e^{2 c_1} x^6+2025 e^{4 c_1}}+675 e^{2 c_1}}-\frac {7 x^2}{15}+\frac {i \left (\sqrt {3}+i\right ) x^4}{60 \sqrt [3]{x^6+15 \sqrt {6 e^{2 c_1} x^6+2025 e^{4 c_1}}+675 e^{2 c_1}}}}\\ y(x)&\to \sqrt {\frac {1}{60} \left (-1-i \sqrt {3}\right ) \sqrt [3]{x^6+15 \sqrt {6 e^{2 c_1} x^6+2025 e^{4 c_1}}+675 e^{2 c_1}}-\frac {7 x^2}{15}+\frac {i \left (\sqrt {3}+i\right ) x^4}{60 \sqrt [3]{x^6+15 \sqrt {6 e^{2 c_1} x^6+2025 e^{4 c_1}}+675 e^{2 c_1}}}}\\ y(x)&\to -\sqrt {\frac {1}{60} i \left (\sqrt {3}+i\right ) \sqrt [3]{x^6+15 \sqrt {6 e^{2 c_1} x^6+2025 e^{4 c_1}}+675 e^{2 c_1}}-\frac {7 x^2}{15}+\frac {\left (-1-i \sqrt {3}\right ) x^4}{60 \sqrt [3]{x^6+15 \sqrt {6 e^{2 c_1} x^6+2025 e^{4 c_1}}+675 e^{2 c_1}}}}\\ y(x)&\to \sqrt {\frac {1}{60} i \left (\sqrt {3}+i\right ) \sqrt [3]{x^6+15 \sqrt {6 e^{2 c_1} x^6+2025 e^{4 c_1}}+675 e^{2 c_1}}-\frac {7 x^2}{15}+\frac {\left (-1-i \sqrt {3}\right ) x^4}{60 \sqrt [3]{x^6+15 \sqrt {6 e^{2 c_1} x^6+2025 e^{4 c_1}}+675 e^{2 c_1}}}} \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x*(6*x**2 + 14*y(x)**2) + (13*x**2 + 30*y(x)**2)*y(x)*Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out