82.53.4 problem Ex. 4

Internal problem ID [19016]
Book : Introductory Course On Differential Equations by Daniel A Murray. Longmans Green and Co. NY. 1924
Section : Chapter IX. Equations of the second order. problems at page 118
Problem number : Ex. 4
Date solved : Tuesday, January 28, 2025 at 12:45:44 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)
 

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

✓ Solution by Mathematica

Time used: 0.056 (sec). Leaf size: 38

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]
 

\[ y(x)\to \frac {1}{a^2 x^2}+c_1 \cos \left (\frac {a}{2 x^2}\right )-c_2 \sin \left (\frac {a}{2 x^2}\right ) \]