Internal problem ID [14882]
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.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_Emden, _Fowler]]
\[ \boxed {x^{2} y^{\prime \prime }-7 y^{\prime } x +25 y=0} \]
✓ Solution by Maple
Time used: 0.0 (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)
\[ y \left (x \right ) = x^{4} \left (c_{1} \sin \left (3 \ln \left (x \right )\right )+c_{2} \cos \left (3 \ln \left (x \right )\right )\right ) \]
✓ Solution by Mathematica
Time used: 0.021 (sec). Leaf size: 26
DSolve[x^2*y''[x]-7*x*y'[x]+25*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to x^4 (c_2 \cos (3 \log (x))+c_1 \sin (3 \log (x))) \]