Internal problem ID [2793]
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 20.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime \prime }-6 y^{\prime \prime }+12 y^{\prime }-8 y=36 \,{\mathrm e}^{2 x} \ln \left (x \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 31
dsolve(diff(y(x),x$3)-6*diff(y(x),x$2)+12*diff(y(x),x)-8*y(x)=36*exp(2*x)*ln(x),y(x), singsol=all)
\[ y \left (x \right ) = {\mathrm e}^{2 x} \left (6 x^{3} \ln \left (x \right )-11 x^{3}+c_{1} +c_{2} x +c_{3} x^{2}\right ) \]
✓ Solution by Mathematica
Time used: 0.009 (sec). Leaf size: 36
DSolve[y'''[x]-6*y''[x]+12*y'[x]-8*y[x]==36*Exp[2*x]*Log[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^{2 x} \left (-11 x^3+6 x^3 \log (x)+c_3 x^2+c_2 x+c_1\right ) \]