Internal problem ID [2300]
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 21.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {x^{2} y^{\prime \prime }-\left (2 m -1\right ) x y^{\prime }+m^{2} y-x^{m} \ln \relax (x )^{k}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 37
dsolve(x^2*diff(y(x),x$2)-(2*m-1)*x*diff(y(x),x)+m^2*y(x)=x^m*(ln(x))^k,y(x), singsol=all)
\[ y \relax (x ) = x^{m} c_{2}+\ln \relax (x ) x^{m} c_{1}+\frac {\ln \relax (x )^{k +2} x^{m}}{k^{2}+3 k +2} \]
✓ Solution by Mathematica
Time used: 0.021 (sec). Leaf size: 35
DSolve[x^2*y''[x]-(2*m-1)*x*y'[x]+m^2*y[x]==x^m*(Log[x])^k,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x^m \left (\frac {\log ^{k+2}(x)}{k^2+3 k+2}+c_2 m \log (x)+c_1\right ) \\ \end{align*}