Internal problem ID [14736]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 4. Higher Order Equations. Exercises 4.7, page 195
Problem number: 27.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {x^{2} y^{\prime \prime }+y^{\prime } x +4 y=8} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 20
dsolve(x^2*diff(y(x),x$2)+x*diff(y(x),x)+4*y(x)=8,y(x), singsol=all)
\[ y \left (x \right ) = c_{2} \sin \left (2 \ln \left (x \right )\right )+\cos \left (2 \ln \left (x \right )\right ) c_{1} +2 \]
✓ Solution by Mathematica
Time used: 0.017 (sec). Leaf size: 23
DSolve[x^2*y''[x]+x*y'[x]+4*y[x]==8,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to c_1 \cos (2 \log (x))+c_2 \sin (2 \log (x))+2 \]