76.13.54 problem 63

Internal problem ID [17636]
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 : 63
Date solved : Tuesday, January 28, 2025 at 10:46:19 AM
CAS classification : [[_Emden, _Fowler]]

\begin{align*} 4 x^{2} y^{\prime \prime }+8 x y^{\prime }+17 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: 0.032 (sec). Leaf size: 23

dsolve([4*x^2*diff(y(x),x$2)+8*x*diff(y(x),x)+17*y(x)=0,y(1) = 2, D(y)(1) = -3],y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.023 (sec). Leaf size: 26

DSolve[{4*x^2*D[y[x],{x,2}]+8*x*D[y[x],x]+17*y[x]==0,{y[1]==2,Derivative[1][y][1] ==-3}},y[x],x,IncludeSingularSolutions -> True]
 

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