74.15.57 problem 57

Internal problem ID [16496]
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 : 57
Date solved : Tuesday, January 28, 2025 at 09:09:42 AM
CAS classification : [[_2nd_order, _exact, _linear, _homogeneous]]

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

✓ Solution by Maple

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

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

\[ y = \frac {c_{1} x +c_{2}}{x^{2}} \]

✓ Solution by Mathematica

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

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

\[ y(x)\to \frac {c_2 x+c_1}{x^2} \]