Internal problem ID [2241]
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 8.3, The Method of Undetermined
Coefficients. page 525
Problem number: Problem 30.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {y^{\prime \prime \prime }+2 y^{\prime \prime }-5 y^{\prime }-6 y-4 x^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 32
dsolve(diff(y(x),x$3)+2*diff(y(x),x$2)-5*diff(y(x),x)-6*y(x)=4*x^2,y(x), singsol=all)
\[ y \relax (x ) = -\frac {2 x^{2}}{3}+\frac {10 x}{9}-\frac {37}{27}+c_{1} {\mathrm e}^{-3 x}+c_{2} {\mathrm e}^{-x}+c_{3} {\mathrm e}^{2 x} \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 43
DSolve[y'''[x]+2*y''[x]-5*y'[x]-6*y[x]==4*x^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {2}{9} (5-3 x) x+c_1 e^{-3 x}+c_2 e^{-x}+c_3 e^{2 x}-\frac {37}{27} \\ \end{align*}