20.9.20 problem Problem 20

Internal problem ID [3764]
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
Date solved : Monday, January 27, 2025 at 08:01:03 AM
CAS classification : [[_3rd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+12 y^{\prime }-8 y&=36 \,{\mathrm e}^{2 x} \ln \left (x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.004 (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)
 

\[ y \left (x \right ) = {\mathrm e}^{2 x} \left (6 x^{3} \ln \left (x \right )-11 x^{3}+c_{1} +c_{2} x^{2}+x c_3 \right ) \]

✓ Solution by Mathematica

Time used: 0.010 (sec). Leaf size: 36

DSolve[D[y[x],{x,3}]-6*D[y[x],{x,2}]+12*D[y[x],x]-8*y[x]==36*Exp[2*x]*Log[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{2 x} \left (-11 x^3+6 x^3 \log (x)+c_3 x^2+c_2 x+c_1\right ) \]