8.7.16 problem 16

Internal problem ID [822]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 5.1, second order linear equations. Page 299
Problem number : 16
Date solved : Wednesday, February 05, 2025 at 04:29:52 AM
CAS classification : [[_Emden, _Fowler], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]

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

With initial conditions

\begin{align*} y \left (1\right )&=2\\ y^{\prime }\left (1\right )&=3 \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 15

dsolve([x^2*diff(y(x),x$2)+x*diff(y(x),x)+y(x)=0,y(1) = 2, D(y)(1) = 3],y(x), singsol=all)
 

\[ y = 3 \sin \left (\ln \left (x \right )\right )+2 \cos \left (\ln \left (x \right )\right ) \]

✓ Solution by Mathematica

Time used: 0.015 (sec). Leaf size: 16

DSolve[{x^2*D[y[x],{x,2}]+x*D[y[x],x]+y[x]==0,{y[1]==2,Derivative[1][y][1]==3}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to 3 \sin (\log (x))+2 \cos (\log (x)) \]