Internal problem ID [2283]
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 19.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }-y-\frac {2 \,{\mathrm e}^{x}}{x^{2}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.012 (sec). Leaf size: 28
dsolve(diff(y(x),x$3)-3*diff(y(x),x$2)+3*diff(y(x),x)-y(x)=2*x^(-2)*exp(x),y(x), singsol=all)
\[ y \relax (x ) = -2 \,{\mathrm e}^{x} \ln \relax (x ) x +c_{1} {\mathrm e}^{x}+c_{2} x \,{\mathrm e}^{x}+c_{3} x^{2} {\mathrm e}^{x} \]
✓ Solution by Mathematica
Time used: 0.376 (sec). Leaf size: 256
DSolve[y'''[x]-6*y''[x]+3*y'[x]-y[x]==2*x^(-2)*Exp[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \text {Root}\left [117 \text {$\#$1}^3+12 \text {$\#$1}+8\&,2\right ] \exp \left (x \text {Root}\left [\text {$\#$1}^3-6 \text {$\#$1}^2+3 \text {$\#$1}-1\&,2\right ]\right ) \text {Ei}\left (x \text {Root}\left [\text {$\#$1}^3+3 \text {$\#$1}^2-6 \text {$\#$1}+3\&,3\right ]\right )+\exp \left (x \text {Root}\left [\text {$\#$1}^3-6 \text {$\#$1}^2+3 \text {$\#$1}-1\&,3\right ]\right ) \left (\text {Root}\left [117 \text {$\#$1}^3+12 \text {$\#$1}+8\&,3\right ] \text {Ei}\left (x \text {Root}\left [\text {$\#$1}^3+3 \text {$\#$1}^2-6 \text {$\#$1}+3\&,2\right ]\right )+c_3\right )+c_2 \exp \left (x \text {Root}\left [\text {$\#$1}^3-6 \text {$\#$1}^2+3 \text {$\#$1}-1\&,2\right ]\right )+\text {Root}\left [117 \text {$\#$1}^3+12 \text {$\#$1}+8\&,1\right ] \text {Ei}\left (x \text {Root}\left [\text {$\#$1}^3+3 \text {$\#$1}^2-6 \text {$\#$1}+3\&,1\right ]\right ) \exp \left (x \text {Root}\left [\text {$\#$1}^3-6 \text {$\#$1}^2+3 \text {$\#$1}-1\&,1\right ]\right )+c_1 \exp \left (x \text {Root}\left [\text {$\#$1}^3-6 \text {$\#$1}^2+3 \text {$\#$1}-1\&,1\right ]\right ) \\ \end{align*}