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Glossary of calc ii exam 2
Created by 35173
- ay'' + by' + cy = 0; r[1], r[2] equal
- y(x) = c[1]e^(r[1]x) + c[2]xe^(r[1]x)
- ay'' + by' + cy = 0; r[1], r[2] imaginary
- y(x) = e^(px)*(c[1]cos(qx) + c[2]sin(qx));
p = -b/2a; q = sqrt(4ac-b^2)/2a; r = p +/- qi - ay'' + by' + cy = 0; r[1], r[2] unequal
- y(x) = c[1]e^(r[1]x) + c[2]e^(r[2]x)
- Euler's method/Step problem
- x[n+1] = x[n] + h;
y[n+1] = y[n] + h*y';
h = step - Linear equation
- y' + P(x)y = Q(x);
P(x) can only have constants and x-variables;
p(x) = e^(P(x)dx);
p(x)y = ~p(x)Q(x)dx
- Newton's law of cooling
- u' = k(u-A);
u = temperature of body, A = temperature of surrounding area - Population Model
- P' = aP - bP^2 = kP(M-P);
M is limiting population - what it approaches - set-up for tank problem
- x(t) is the amount of salt in tank 1 after time t;
x' = (gal/min input)-(gal/min output);
output = (v[2])(x(t)/(V-(v[1]-v[2]))
