58.2.18 problem 19

Internal problem ID [9141]
Book : Second order enumerated odes
Section : section 2
Problem number : 19
Date solved : Monday, January 27, 2025 at 05:48:50 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} x^{6} y^{\prime \prime }+3 x^{5} y^{\prime }+a^{2} y&=\frac {1}{x^{2}} \end{align*}

✓ Solution by Maple

Time used: 0.006 (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)
 

\[ y = \sin \left (\frac {a}{2 x^{2}}\right ) c_{2} +\cos \left (\frac {a}{2 x^{2}}\right ) c_{1} +\frac {1}{a^{2} x^{2}} \]

✓ Solution by Mathematica

Time used: 0.071 (sec). Leaf size: 104

DSolve[x^6*D[y[x],{x,2}]+3*x^5*D[y[x],x]+a^2*y[x]==1/x^2,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -\sin \left (\frac {a}{2 x^2}\right ) \int _1^x\frac {\cos \left (\frac {a}{2 K[1]^2}\right )}{a K[1]^5}dK[1]+\frac {-2 a^3 c_2 x^2 \sin \left (\frac {a}{2 x^2}\right )-2 x^2 \sin \left (\frac {a}{x^2}\right )+a \cos \left (\frac {a}{x^2}\right )+a}{2 a^3 x^2}+c_1 \cos \left (\frac {a}{2 x^2}\right ) \]