Femtobytes
Problem type

Second order equation with constant coefficients

What it solves
Solve a y'' + b y' + c y = 0 with starting values for y and y': write the characteristic equation, handle whichever of the three cases arises (two real roots, a repeated root, or a complex pair), fit the constants, and check the answer exactly.
Subject
Differential Equations
Topic
Second order equations
Also called
auxiliary equation, characteristic equation, second order ODE, constant coefficients
Your problem

Solve this starting value problem.

y′′+2y′+5y=0,y(0)=1,y′(0)=0y'' + 2 y' + 5 y = 0, \qquad y(0) = 1, \quad y'(0) = 0
Invent a new one: