68.15.67 problem 66 (a)

Internal problem ID [17793]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 4. Higher Order Equations. Exercises 4.7, page 195
Problem number : 66 (a)
Date solved : Thursday, October 02, 2025 at 02:28:18 PM
CAS classification : [[_Emden, _Fowler], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]

\begin{align*} 6 x^{2} y^{\prime \prime }+5 x y^{\prime }-y&=0 \end{align*}

With initial conditions

\begin{align*} y \left (1\right )&=a \\ y^{\prime }\left (1\right )&=b \\ \end{align*}

✓ Maple. Time used: 0.052 (sec). Leaf size: 25

ode:=6*x^2*diff(diff(y(x),x),x)+5*x*diff(y(x),x)-y(x) = 0; 
ic:=[y(1) = a, D(y)(1) = b]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = \frac {\frac {2 \left (a +3 b \right ) x^{{5}/{6}}}{5}+\frac {3 a}{5}-\frac {6 b}{5}}{x^{{1}/{3}}} \]

✓ Mathematica. Time used: 0.009 (sec). Leaf size: 36

ode=6*x^2*D[y[x],{x,2}]+5*x*D[y[x],x]-y[x]==0; 
ic={y[1]==a,Derivative[1][y][1]==b}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {a \left (2 x^{5/6}+3\right )+6 b \left (x^{5/6}-1\right )}{5 \sqrt [3]{x}} \end{align*}

✓ Sympy. Time used: 0.110 (sec). Leaf size: 32

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(6*x**2*Derivative(y(x), (x, 2)) + 5*x*Derivative(y(x), x) - y(x),0) 
ics = {y(1): a, Subs(Derivative(y(x), x), x, 1): b} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \sqrt {x} \left (\frac {2 a}{5} + \frac {6 b}{5}\right ) + \frac {\frac {3 a}{5} - \frac {6 b}{5}}{\sqrt [3]{x}} \]