Internal problem ID [2750]
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]]
\[ \boxed {y^{\prime \prime \prime }+2 y^{\prime \prime }-5 y^{\prime }-6 y=4 x^{2}} \]
✓ Solution by Maple
Time used: 0.016 (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)
\[ y \left (x \right ) = -\frac {2 x^{2}}{3}+\frac {10 x}{9}-\frac {37}{27}+c_{1} {\mathrm e}^{-3 x}+{\mathrm e}^{-x} c_{2} +c_{3} {\mathrm e}^{2 x} \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 45
DSolve[y'''[x]+2*y''[x]-5*y'[x]-6*y[x]==4*x^2,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -\frac {2 x^2}{3}+\frac {10 x}{9}+c_1 e^{-3 x}+c_2 e^{-x}+c_3 e^{2 x}-\frac {37}{27} \]