Internal problem ID [2294]
Book: Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition,
2015
Section: Chapter 8, Linear differential equations of order n. Section 8.8, A Differential Equation with
Nonconstant Coefficients. page 567
Problem number: Problem 15.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _exact, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {x^{2} y^{\prime \prime }+4 y^{\prime } x +2 y-\cos \relax (x )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 22
dsolve(x^2*diff(y(x),x$2)+4*x*diff(y(x),x)+2*y(x)=cos(x),y(x), singsol=all)
\[ y \relax (x ) = \frac {c_{1}}{x}-\frac {\cos \relax (x )}{x^{2}}+\frac {c_{2}}{x^{2}} \]
✓ Solution by Mathematica
Time used: 0.011 (sec). Leaf size: 20
DSolve[x^2*y''[x]+4*x*y'[x]+2*y[x]==Cos[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {-\cos (x)+c_2 x+c_1}{x^2} \\ \end{align*}