74.15.33 problem 33

Internal problem ID [16472]
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 : 33
Date solved : Tuesday, January 28, 2025 at 09:08:51 AM
CAS classification : [[_Emden, _Fowler], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]

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

With initial conditions

\begin{align*} y \left (1\right )&=-1\\ y^{\prime }\left (1\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 11

dsolve([x^2*diff(y(x),x$2)+x*diff(y(x),x)+4*y(x)=0,y(1) = -1, D(y)(1) = 0],y(x), singsol=all)
 

\[ y = -\cos \left (2 \ln \left (x \right )\right ) \]

✓ Solution by Mathematica

Time used: 0.018 (sec). Leaf size: 12

DSolve[{x^2*D[y[x],{x,2}]+x*D[y[x],x]+4*y[x]==0,{y[1]==-1,Derivative[1][y][1]==0}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -\cos (2 \log (x)) \]