74.15.34 problem 34

Internal problem ID [16473]
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 : 34
Date solved : Tuesday, January 28, 2025 at 09:08:53 AM
CAS classification : [[_Emden, _Fowler], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]

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

With initial conditions

\begin{align*} y \left (1\right )&=0\\ y^{\prime }\left (1\right )&=2 \end{align*}

✓ Solution by Maple

Time used: 0.049 (sec). Leaf size: 15

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

\[ y = \sqrt {2}\, \sin \left (\sqrt {2}\, \ln \left (x \right )\right ) \]

✓ Solution by Mathematica

Time used: 0.024 (sec). Leaf size: 20

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

\[ y(x)\to \sqrt {2} \sin \left (\sqrt {2} \log (x)\right ) \]