Internal problem ID [5422]
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.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {x^{8} y^{\prime \prime }+4 y^{\prime } x^{7}+y=\frac {1}{x^{3}}} \]
✓ Solution by Maple
Time used: 0.015 (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)
\[ y \left (x \right ) = \sin \left (\frac {1}{3 x^{3}}\right ) c_{2} +\cos \left (\frac {1}{3 x^{3}}\right ) c_{1} +\frac {1}{x^{3}} \]
✓ Solution by Mathematica
Time used: 0.057 (sec). Leaf size: 32
DSolve[x^8*y''[x]+4*x^7*y'[x]+y[x]==1/x^3,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{x^3}+c_1 \cos \left (\frac {1}{3 x^3}\right )-c_2 \sin \left (\frac {1}{3 x^3}\right ) \]