Internal problem ID [5421]
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: 30.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {x^{4} y^{\prime \prime }+2 y^{\prime } x^{3}+y=\frac {x +1}{x}} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 24
dsolve(x^4*diff(y(x),x$2)+2*x^3*diff(y(x),x)+y(x)=(1+x)/x,y(x), singsol=all)
\[ y \left (x \right ) = \sin \left (\frac {1}{x}\right ) c_{2} +\cos \left (\frac {1}{x}\right ) c_{1} +\frac {x +1}{x} \]
✓ Solution by Mathematica
Time used: 0.072 (sec). Leaf size: 25
DSolve[x^4*y''[x]+2*x^3*y'[x]+y[x]==(1+x)/x,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{x}+c_1 \cos \left (\frac {1}{x}\right )-c_2 \sin \left (\frac {1}{x}\right )+1 \]