83.7.7 problem 5 (a)

Internal problem ID [19054]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter II. Equations of first order and first degree. Exercise II (F) at page 24
Problem number : 5 (a)
Date solved : Monday, March 31, 2025 at 06:37:14 PM
CAS classification : [[_homogeneous, `class G`], _rational, [_Abel, `2nd type`, `class B`]]

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

✓ Maple. Time used: 0.185 (sec). Leaf size: 1165

ode:=y(x)^2+2*x^2*y(x)+(2*x^3-x*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: 47.865 (sec). Leaf size: 546

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

\begin{align*} y(x)\to 4 x^2+\frac {\sqrt [3]{-16 x^6+e^{3 c_1} x^3+\sqrt {e^{3 c_1} x^6 \left (-32 x^3+e^{3 c_1}\right )}}}{\sqrt [3]{2}}+\frac {4 \sqrt [3]{2} x^4}{\sqrt [3]{-16 x^6+e^{3 c_1} x^3+\sqrt {e^{3 c_1} x^6 \left (-32 x^3+e^{3 c_1}\right )}}} \\ y(x)\to 4 x^2+\frac {i \left (\sqrt {3}+i\right ) \sqrt [3]{-16 x^6+e^{3 c_1} x^3+\sqrt {e^{3 c_1} x^6 \left (-32 x^3+e^{3 c_1}\right )}}}{2 \sqrt [3]{2}}-\frac {2 \sqrt [3]{2} \left (1+i \sqrt {3}\right ) x^4}{\sqrt [3]{-16 x^6+e^{3 c_1} x^3+\sqrt {e^{3 c_1} x^6 \left (-32 x^3+e^{3 c_1}\right )}}} \\ y(x)\to 4 x^2-\frac {\left (1+i \sqrt {3}\right ) \sqrt [3]{-16 x^6+e^{3 c_1} x^3+\sqrt {e^{3 c_1} x^6 \left (-32 x^3+e^{3 c_1}\right )}}}{2 \sqrt [3]{2}}+\frac {2 i \sqrt [3]{2} \left (\sqrt {3}+i\right ) x^4}{\sqrt [3]{-16 x^6+e^{3 c_1} x^3+\sqrt {e^{3 c_1} x^6 \left (-32 x^3+e^{3 c_1}\right )}}} \\ y(x)\to \frac {2 \left (\sqrt [3]{-x^6}+x^2\right )^2}{\sqrt [3]{-x^6}} \\ y(x)\to \left (-1-i \sqrt {3}\right ) \sqrt [3]{-x^6}+4 x^2+\frac {\left (1-i \sqrt {3}\right ) \left (-x^6\right )^{2/3}}{x^2} \\ y(x)\to i \left (\sqrt {3}+i\right ) \sqrt [3]{-x^6}+4 x^2+\frac {\left (1+i \sqrt {3}\right ) \left (-x^6\right )^{2/3}}{x^2} \\ \end{align*}

✗ Sympy

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

Timed Out