Internal problem ID [14737]
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: 28.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {x^{2} y^{\prime \prime }+y^{\prime } x +36 y=x^{2}} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 24
dsolve(x^2*diff(y(x),x$2)+x*diff(y(x),x)+36*y(x)=x^2,y(x), singsol=all)
\[ y \left (x \right ) = \sin \left (6 \ln \left (x \right )\right ) c_{2} +\cos \left (6 \ln \left (x \right )\right ) c_{1} +\frac {x^{2}}{40} \]
✓ Solution by Mathematica
Time used: 0.057 (sec). Leaf size: 29
DSolve[x^2*y''[x]+x*y'[x]+36*y[x]==x^2,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {x^2}{40}+c_1 \cos (6 \log (x))+c_2 \sin (6 \log (x)) \]