76.13.56 problem 65

Internal problem ID [17638]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 4. Second order linear equations. Section 4.3 (Linear homogeneous equations with constant coefficients). Problems at page 239
Problem number : 65
Date solved : Tuesday, January 28, 2025 at 10:46:25 AM
CAS classification : [[_Emden, _Fowler]]

\begin{align*} x^{2} y^{\prime \prime }+3 x y^{\prime }+5 y&=0 \end{align*}

With initial conditions

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

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 13

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

\[ y = \frac {\cos \left (2 \ln \left (x \right )\right )}{x} \]

✓ Solution by Mathematica

Time used: 0.020 (sec). Leaf size: 14

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

\[ y(x)\to \frac {\cos (2 \log (x))}{x} \]