60.1.393 problem 404

Internal problem ID [10407]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 404
Date solved : Wednesday, March 05, 2025 at 10:45:00 AM
CAS classification : [[_homogeneous, `class G`]]

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

✓ Maple. Time used: 0.186 (sec). Leaf size: 479

ode:=a*diff(y(x),x)^2+b*x^2*diff(y(x),x)+c*x*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 6.18 (sec). Leaf size: 313

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

\begin{align*} \text {Solve}\left [\frac {-6 b \text {arctanh}\left (\frac {b x \sqrt {b^2 x^4-4 a c x y(x)}}{b^2 x^3-4 a c y(x)}\right )+(6 b+4 c) \text {arctanh}\left (\frac {x^2 (3 b+2 c)}{3 \sqrt {b^2 x^4-4 a c x y(x)}}\right )+(3 b+2 c) \log \left (9 a y(x)+3 b x^3+c x^3\right )}{6 (3 b+c)}+\frac {b \log (6 b y(x)+2 c y(x))}{2 (3 b+c)}&=c_1,y(x)\right ] \\ \text {Solve}\left [\frac {6 b \text {arctanh}\left (\frac {b x \sqrt {b^2 x^4-4 a c x y(x)}}{b^2 x^3-4 a c y(x)}\right )-2 (3 b+2 c) \text {arctanh}\left (\frac {x^2 (3 b+2 c)}{3 \sqrt {b^2 x^4-4 a c x y(x)}}\right )+(3 b+2 c) \log \left (9 a y(x)+3 b x^3+c x^3\right )}{6 (3 b+c)}+\frac {b \log (6 b y(x)+2 c y(x))}{2 (3 b+c)}&=c_1,y(x)\right ] \\ y(x)\to 0 \\ \end{align*}

✗ Sympy

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

Timed Out