20.10.9 problem Problem 22

Internal problem ID [3781]
Book : Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition, 2015
Section : Chapter 8, Linear differential equations of order n. Section 8.8, A Differential Equation with Nonconstant Coefficients. page 567
Problem number : Problem 22
Date solved : Monday, January 27, 2025 at 08:02:08 AM
CAS classification : [[_Emden, _Fowler]]

\begin{align*} x^{2} y^{\prime \prime }-x y^{\prime }+5 y&=0 \end{align*}

With initial conditions

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

✓ Solution by Maple

Time used: 0.018 (sec). Leaf size: 20

dsolve([x^2*diff(y(x),x$2)-x*diff(y(x),x)+5*y(x)=0,y(1) = 2^(1/2), D(y)(1) = 3*2^(1/2)],y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.026 (sec). Leaf size: 23

DSolve[{x^2*D[y[x],{x,2}]-x*D[y[x],x]+5*y[x]==0,{y[1]==Sqrt[2],Derivative[1][y][1]==3*Sqrt[2]}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \sqrt {2} x (\sin (2 \log (x))+\cos (2 \log (x))) \]