74.18.55 problem 61

Internal problem ID [16612]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 4. Higher Order Equations. Chapter 4 review exercises, page 219
Problem number : 61
Date solved : Tuesday, January 28, 2025 at 09:12:46 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)
 

\[ y = x^{4} \left (c_{1} \sin \left (3 \ln \left (x \right )\right )+c_{2} \cos \left (3 \ln \left (x \right )\right )\right ) \]

✓ 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]
 

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