Internal problem ID [4104]
Book: Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section: Chapter 4. Higher order linear differential equations. Lesson 21. Undetermined
Coefficients
Problem number: Exercise 21.9, page 231.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+y^{\prime }+y-x^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.003 (sec). Leaf size: 37
dsolve(diff(y(x),x$2)+diff(y(x),x)+y(x)=x^2,y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{-\frac {x}{2}} \sin \left (\frac {\sqrt {3}\, x}{2}\right ) c_{2}+{\mathrm e}^{-\frac {x}{2}} \cos \left (\frac {\sqrt {3}\, x}{2}\right ) c_{1}+x^{2}-2 x \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 48
DSolve[y''[x]+y'[x]+y[x]==x^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to (x-2) x+e^{-x/2} \left (c_2 \cos \left (\frac {\sqrt {3} x}{2}\right )+c_1 \sin \left (\frac {\sqrt {3} x}{2}\right )\right ) \\ \end{align*}