74.15.1 problem 1

Internal problem ID [16440]
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 : 1
Date solved : Tuesday, January 28, 2025 at 09:07:59 AM
CAS classification : [[_Emden, _Fowler], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]

\begin{align*} 4 x^{2} y^{\prime \prime }-8 x y^{\prime }+5 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 15

dsolve(4*x^2*diff(y(x),x$2)-8*x*diff(y(x),x)+5*y(x)=0,y(x), singsol=all)
 

\[ y = \sqrt {x}\, \left (c_{2} x^{2}+c_{1} \right ) \]

✓ Solution by Mathematica

Time used: 0.012 (sec). Leaf size: 20

DSolve[4*x^2*D[y[x],{x,2}]-8*x*D[y[x],x]+5*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \sqrt {x} \left (c_2 x^2+c_1\right ) \]