60.1.374 problem 383

Internal problem ID [10388]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 383
Date solved : Sunday, March 30, 2025 at 04:34:23 PM
CAS classification : [[_homogeneous, `class G`]]

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

✗ Maple

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

\[ \text {No solution found} \]

✓ Mathematica. Time used: 10.174 (sec). Leaf size: 1118

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

\begin{align*} \text {Solution too large to show}\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*Derivative(y(x), x) + b*y(x) + c*x**2 + Derivative(y(x), x)**2,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out