Internal problem ID [6703]
Book: Second order enumerated odes
Section: section 2
Problem number: 19.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {x^{6} y^{\prime \prime }+3 x^{5} y^{\prime }+a^{2} y-\frac {1}{x^{2}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 30
dsolve(x^6*diff(y(x),x$2)+3*x^5*diff(y(x),x)+a^2*y(x)=1/x^2,y(x), singsol=all)
\[ y \relax (x ) = \sin \left (\frac {a}{2 x^{2}}\right ) c_{2}+\cos \left (\frac {a}{2 x^{2}}\right ) c_{1}+\frac {1}{a^{2} x^{2}} \]
✓ Solution by Mathematica
Time used: 0.039 (sec). Leaf size: 38
DSolve[x^6*y''[x]+3*x^5*y'[x]+a^2*y[x]==1/x^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{a^2 x^2}+c_1 \cos \left (\frac {a}{2 x^2}\right )-c_2 \sin \left (\frac {a}{2 x^2}\right ) \\ \end{align*}