Internal problem ID [4647]
Book: Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section: Chapter 4. Higher order linear differential equations. Lesson 22. Variation of
Parameters
Problem number: Exercise 22, problem 17, page 240.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _exact, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }-\frac {2 y^{\prime }}{x}+\frac {2 y}{x^{2}}=\ln \left (x \right ) x} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 25
dsolve(diff(y(x),x$2)-2/x*diff(y(x),x)+2/x^2*y(x)=x*ln(x),y(x), singsol=all)
\[ y \left (x \right ) = \frac {\ln \left (x \right ) x^{3}}{2}-\frac {3 x^{3}}{4}+c_{2} x^{2}+c_{1} x \]
✓ Solution by Mathematica
Time used: 0.014 (sec). Leaf size: 32
DSolve[y''[x]-2/x*y'[x]+2/x^2*y[x]==x*Log[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{4} x \left (-3 x^2+2 x^2 \log (x)+4 c_2 x+4 c_1\right ) \]