56.1.68 problem 68

Internal problem ID [8780]
Book : Own collection of miscellaneous problems
Section : section 1.0
Problem number : 68
Date solved : Sunday, March 30, 2025 at 01:35:31 PM
CAS classification : [[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]

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

✓ Maple. Time used: 0.029 (sec). Leaf size: 68

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

\begin{align*} a \int _{}^{y}\frac {1}{\sqrt {a \left (2 c \ln \left (\textit {\_a} \right )+c_1 a -2 b \textit {\_a} \right )}}d \textit {\_a} -x -c_2 &= 0 \\ -a \int _{}^{y}\frac {1}{\sqrt {a \left (2 c \ln \left (\textit {\_a} \right )+c_1 a -2 b \textit {\_a} \right )}}d \textit {\_a} -x -c_2 &= 0 \\ \end{align*}

✓ Mathematica. Time used: 0.448 (sec). Leaf size: 43

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

\[ \text {Solve}\left [\int _1^{y(x)}\frac {1}{\sqrt {c_1+\frac {2 (c \log (K[1])-b K[1])}{a}}}dK[1]{}^2=(x+c_2){}^2,y(x)\right ] \]

✗ Sympy

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

Timed Out