8.9.17 problem 53

Internal problem ID [861]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 5.3, second order linear equations. Page 323
Problem number : 53
Date solved : Wednesday, February 05, 2025 at 04:34:38 AM
CAS classification : [[_Emden, _Fowler]]

\begin{align*} x^{2} y^{\prime \prime }+7 x y^{\prime }+25 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 23

dsolve(x^2*diff(y(x),x$2)+7*x*diff(y(x),x)+25*y(x)=0,y(x), singsol=all)
 

\[ y = \frac {c_1 \sin \left (4 \ln \left (x \right )\right )+c_2 \cos \left (4 \ln \left (x \right )\right )}{x^{3}} \]

✓ Solution by Mathematica

Time used: 0.020 (sec). Leaf size: 26

DSolve[x^2*D[y[x],{x,2}]+7*x*D[y[x],x]+25*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {c_2 \cos (4 \log (x))+c_1 \sin (4 \log (x))}{x^3} \]