Internal problem ID [14112]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 1. Introduction to Differential Equations. Review exercises, page
23
Problem number: 12.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }+2 y^{\prime }+2 y=x} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 25
dsolve(diff(y(x),x$2)+2*diff(y(x),x)+2*y(x)=x,y(x), singsol=all)
\[ y \left (x \right ) = {\mathrm e}^{-x} \sin \left (x \right ) c_{2} +{\mathrm e}^{-x} \cos \left (x \right ) c_{1} -\frac {1}{2}+\frac {x}{2} \]
✓ Solution by Mathematica
Time used: 0.015 (sec). Leaf size: 33
DSolve[y''[x]+2*y'[x]+2*y[x]==x,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {x-1}{2}+c_2 e^{-x} \cos (x)+c_1 e^{-x} \sin (x) \]