50.1.70 problem 70

Internal problem ID [10068]
Book : Own collection of miscellaneous problems
Section : section 1.0
Problem number : 70
Date solved : Tuesday, September 30, 2025 at 06:51:59 PM
CAS classification : [[_2nd_order, _quadrature]]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 22

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

\begin{align*} y &= 0 \\ y &= -\frac {b \,x^{2}}{2 a}+c_1 x +c_2 \\ \end{align*}

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 28

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

\begin{align*} y(x)&\to 0\\ y(x)&\to -\frac {b x^2}{2 a}+c_2 x+c_1 \end{align*}

✓ Sympy. Time used: 0.141 (sec). Leaf size: 19

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

\[ \left [ y{\left (x \right )} = C_{1} + C_{2} x - \frac {b x^{2}}{2 a}, \ y{\left (x \right )} = 0\right ] \]