74.15.3 problem 3

Internal problem ID [16442]
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 : 3
Date solved : Tuesday, January 28, 2025 at 09:08:02 AM
CAS classification : [[_Emden, _Fowler]]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 13

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

\[ y = x \left (c_{2} x^{3}+c_{1} \right ) \]

✓ Solution by Mathematica

Time used: 0.011 (sec). Leaf size: 16

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

\[ y(x)\to x \left (c_2 x^3+c_1\right ) \]