74.15.67 problem 66 (a)

Internal problem ID [16506]
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 : Tuesday, January 28, 2025 at 09:09:54 AM
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*}

✓ Solution by Maple

Time used: 0.036 (sec). Leaf size: 25

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

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

✓ Solution by Mathematica

Time used: 0.014 (sec). Leaf size: 36

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

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