83.4.2 problem 1 (b)

Internal problem ID [21929]
Book : Differential Equations By Kaj L. Nielsen. Second edition 1966. Barnes and nobel. 66-28306
Section : Chapter III. First order differential equations of the first degree. Ex. V at page 42
Problem number : 1 (b)
Date solved : Thursday, October 02, 2025 at 08:13:23 PM
CAS classification : [[_homogeneous, `class A`], _exact, _rational, _dAlembert]

\begin{align*} a \,x^{2}+2 b x y+c y^{2}+\left (b \,x^{2}+2 c x y+y^{2}\right ) y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.013 (sec). Leaf size: 878

ode:=x^2*a+2*b*x*y(x)+c*y(x)^2+(b*x^2+2*c*x*y(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: 60.209 (sec). Leaf size: 601

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

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

✗ Sympy

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

Timed Out