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]]
\[ \boxed {x^{2} y^{\prime \prime }-\left (2 m -1\right ) x y^{\prime }+m^{2} y-x^{m} \ln \left (x \right )^{k}=0} \]
✓ Solution by Maple
Time used: 0.0 (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)
\[ y \left (x \right ) = x^{m} c_{2} +\ln \left (x \right ) x^{m} c_{1} +\frac {x^{m} \ln \left (x \right )^{k +2}}{k^{2}+3 k +2} \]
✓ Solution by Mathematica
Time used: 0.022 (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*}