Internal problem ID [2741]
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 8.1, General Theory for
Linear Differential Equations. page 502
Problem number: Problem 39.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }+y^{\prime }-2 y=4 x^{2}+5} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 38
dsolve(diff(y(x),x$2)+diff(y(x),x)-2*y(x)=4*x^2+5,y(x), singsol=all)
\[ y \left (x \right ) = \frac {\left (-4 x^{2}-4 x -11\right ) {\mathrm e}^{-2 x} {\mathrm e}^{2 x}}{2}+\left (c_{1} {\mathrm e}^{3 x}+c_{2} \right ) {\mathrm e}^{-2 x} \]
✓ Solution by Mathematica
Time used: 0.014 (sec). Leaf size: 31
DSolve[y''[x]+y'[x]-2*y[x]==4*x^2+5,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -2 x^2-2 x+c_1 e^{-2 x}+c_2 e^x-\frac {11}{2} \]