Internal problem ID [2802]
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 14.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _exact, _linear, _nonhomogeneous]]
\[ \boxed {x^{2} y^{\prime \prime }+4 x y^{\prime }+2 y=4 \ln \left (x \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 20
dsolve(x^2*diff(y(x),x$2)+4*x*diff(y(x),x)+2*y(x)=4*ln(x),y(x), singsol=all)
\[ y \left (x \right ) = 2 \ln \left (x \right )+\frac {c_{1}}{x}-3+\frac {c_{2}}{x^{2}} \]
✓ Solution by Mathematica
Time used: 0.016 (sec). Leaf size: 23
DSolve[x^2*y''[x]+4*x*y'[x]+2*y[x]==4*Log[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {c_1}{x^2}+2 \log (x)+\frac {c_2}{x}-3 \]