Internal problem ID [2787]
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 8.7, The Variation of
Parameters Method. page 556
Problem number: Problem 13.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }-2 y^{\prime }+y=\frac {4 \,{\mathrm e}^{x} \ln \left (x \right )}{x^{3}}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 29
dsolve(diff(y(x),x$2)-2*diff(y(x),x)+y(x)=4*exp(x)*x^(-3)*ln(x),y(x), singsol=all)
\[ y \left (x \right ) = {\mathrm e}^{x} c_{2} +x \,{\mathrm e}^{x} c_{1} +\frac {2 \,{\mathrm e}^{x} \ln \left (x \right )+3 \,{\mathrm e}^{x}}{x} \]
✓ Solution by Mathematica
Time used: 0.036 (sec). Leaf size: 28
DSolve[y''[x]-2*y'[x]+y[x]==4*Exp[x]*x^(-3)*Log[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {e^x \left (c_2 x^2+2 \log (x)+c_1 x+3\right )}{x} \]