54.3.128 problem 1142

Internal problem ID [12423]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1142
Date solved : Friday, October 03, 2025 at 03:19:06 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} 5 \left (a x +b \right ) y^{\prime \prime }+8 a y^{\prime }+c \left (a x +b \right )^{{1}/{5}} y&=0 \end{align*}

✓ Maple. Time used: 0.055 (sec). Leaf size: 59

ode:=5*(a*x+b)*diff(diff(y(x),x),x)+8*a*diff(y(x),x)+c*(a*x+b)^(1/5)*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {c_1 \sinh \left (\frac {\left (a x +b \right )^{{3}/{5}} \sqrt {5}\, \sqrt {-c}}{3 a}\right )+c_2 \cosh \left (\frac {\left (a x +b \right )^{{3}/{5}} \sqrt {5}\, \sqrt {-c}}{3 a}\right )}{\left (a x +b \right )^{{3}/{5}}} \]

✓ Mathematica. Time used: 0.044 (sec). Leaf size: 89

ode=c*(b + a*x)^(1/5)*y[x] + 8*a*D[y[x],x] + 5*(b + a*x)*D[y[x],{x,2}] == 0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {3 a \left (2 c_1 \cos \left (\frac {\sqrt {5} \sqrt {c} (a x+b)^{3/5}}{3 a}\right )+c_2 \sin \left (\frac {\sqrt {5} \sqrt {c} (a x+b)^{3/5}}{3 a}\right )\right )}{\sqrt {5} \sqrt {c} (a x+b)^{3/5}} \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
a = symbols("a") 
b = symbols("b") 
c = symbols("c") 
y = Function("y") 
ode = Eq(8*a*Derivative(y(x), x) + c*(a*x + b)**(1/5)*y(x) + (5*a*x + 5*b)*Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

False