40.13.11 problem 31

Internal problem ID [6765]
Book : Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres. McGraw Hill 1952
Section : Chapter 18. Linear equations with variable coefficients (Equations of second order). Supplemetary problems. Page 120
Problem number : 31
Date solved : Monday, January 27, 2025 at 02:29:39 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} x^{8} y^{\prime \prime }+4 x^{7} y^{\prime }+y&=\frac {1}{x^{3}} \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 24

dsolve(x^8*diff(y(x),x$2)+4*x^7*diff(y(x),x)+y(x)=1/x^3,y(x), singsol=all)
 

\[ y = \sin \left (\frac {1}{3 x^{3}}\right ) c_2 +\cos \left (\frac {1}{3 x^{3}}\right ) c_1 +\frac {1}{x^{3}} \]

✓ Solution by Mathematica

Time used: 0.057 (sec). Leaf size: 32

DSolve[x^8*D[y[x],{x,2}]+4*x^7*D[y[x],x]+y[x]==1/x^3,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{x^3}+c_1 \cos \left (\frac {1}{3 x^3}\right )-c_2 \sin \left (\frac {1}{3 x^3}\right ) \]