Flashcards
Differential Equations
Cards in this deck (16)
- 1The degree of a derivative is _______The number of times the dependant variable and its derivatives has been differentiated to reach the given derivative
- 2The order of a differential equations is _______Equivalent to the degree of the derivative with the highest degree
- 3A differential equation is linear when.The dependant variable and its derivatives occur to the first power only.
- 4A first order differential equation is of the variable separable type when dy/dx = h(x,y) can be written asdy/dx = f(x)g(y)
- 5What is an exact equation (in terms of 1st order ODEs)an equation that can be solved by intergrating both sides using 'inverse product rule'. e.g
x(dy/dx) + y = 4X - 6How do we integrate none exact 1st order ODEsUse the integrating factor to make them exact
- 7what is the intergrating factor from the general 1st order ODE dy/dx + f(x)y = g(x)exp[ ∫ f(x) ]
- 8The 2nd order ODE a (d2y/dx2) + b (dy/dx) + cy = f(x) is homogeneous when __________f(x) = 0
- 9The 2nd order ODE a (d2y/dx2) + b (dy/dx) + cy = f(x) is constant coefficient when __________a,b and c are all arbitrary constants
- 10When finding the complimentary solution to a constant coefficient linear 2nd order ODEs we assume that y takes the form ________________ and make a complimentary functiony = exp(kx)
and therefore its d
dy/dx = k.exp(kx)
d2y/dx2 = k^(2).exp(kx) - 11When finding the complimentary solution to a constant coefficient linear 2nd order ODE and we find our quadratic equation has 2 real roots, k1 and k2, we can say that y =A.exp(k1x)+B.exp(k2x)
where A and B are constant to be found - 12When finding the complimentary solution to a constant coefficient linear 2nd order ODE and we find our quadratic equation has 1 repeated root, K we can say that y =A.exp(kx)+Bx.exp(kx)
where A and B are constant to be found - 13When finding the complimentary solution to a constant coefficient linear 2nd order ODE and we find our quadratic equation has a complex root, K=a+bi ; b>0 we can say that y =exp(ax).[cos(bx)+sin(bx)]
- 14the general solution to an inhomogenous constant coefficient linear 2nd order ODE. can be written as the sum of what 2 thingsThe complimentary and particular solutions.
y = yc + yp - 15What is the trial solution of y for the particular solution when f(x) = constant, c linear, ax+b polynomial, ax^(r) + ... + bx + cY =
___________________________________________________
k
Ax+B
Ax^(r) + ... + Bx + k - 16What is the trial solution for the particular solution when f(x) = a cos kx a sin kx a.exp(kx)Y =
___________________________________________________
A cos kx + B sin kx
A cos kx + B sin kx
A.exp(kx)
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- 1st Year Part A (Maths 2) Flashcards on Differential Equations, created by Ben Jenner on 30/03/2016.
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- Ben Jenner
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