54.1.298 problem 304

Internal problem ID [11612]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 304
Date solved : Tuesday, September 30, 2025 at 09:38:16 PM
CAS classification : [[_homogeneous, `class G`], _rational]

\begin{align*} \left (10 x^{3} y^{2}+x^{2} y+2 x \right ) y^{\prime }+5 x^{2} y^{3}+x y^{2}&=0 \end{align*}

✓ Maple. Time used: 0.188 (sec). Leaf size: 55

ode:=(10*x^3*y(x)^2+x^2*y(x)+2*x)*diff(y(x),x)+5*x^2*y(x)^3+x*y(x)^2 = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {\tan \left (\operatorname {RootOf}\left (\sqrt {10}\, \ln \left (\frac {\tan \left (\textit {\_Z} \right )^{2} \sec \left (\textit {\_Z} \right )^{2}}{x^{2}}\right )+2 \sqrt {10}\, \ln \left (2\right )-\sqrt {10}\, \ln \left (5\right )+2 \sqrt {10}\, c_1 +2 \textit {\_Z} \right )\right ) \sqrt {10}}{5 x} \]

✓ Mathematica. Time used: 0.176 (sec). Leaf size: 44

ode=(10*x^3*y[x]^2+x^2*y[x]+2*x)*D[y[x],x]+5*x^2*y[x]^3+x*y[x]^2==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ \text {Solve}\left [y(x) \sqrt {5 x^2 y(x)^2+2} e^{\frac {\arctan \left (\sqrt {\frac {5}{2}} x y(x)\right )}{\sqrt {10}}}=c_1,y(x)\right ] \]

✓ Sympy. Time used: 0.769 (sec). Leaf size: 46

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(5*x**2*y(x)**3 + x*y(x)**2 + (10*x**3*y(x)**2 + x**2*y(x) + 2*x)*Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ - \log {\left (x \right )} + \log {\left (x y{\left (x \right )} \right )} + \frac {\log {\left (x^{2} y^{2}{\left (x \right )} + \frac {2}{5} \right )}}{2} + \frac {\sqrt {10} \operatorname {atan}{\left (\frac {\sqrt {10} x y{\left (x \right )}}{2} \right )}}{10} = C_{1} \]