Internal problem ID [2803]
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]]
\[ \boxed {x^{2} y^{\prime \prime }+4 x y^{\prime }+2 y=\cos \left (x \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 17
dsolve(x^2*diff(y(x),x$2)+4*x*diff(y(x),x)+2*y(x)=cos(x),y(x), singsol=all)
\[ y \left (x \right ) = \frac {c_{2} +c_{1} x -\cos \left (x \right )}{x^{2}} \]
✓ Solution by Mathematica
Time used: 0.027 (sec). Leaf size: 20
DSolve[x^2*y''[x]+4*x*y'[x]+2*y[x]==Cos[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {-\cos (x)+c_2 x+c_1}{x^2} \]