Numerical Methods in Context (AQA A-Level Mathematics): Quizzes

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Numerical Methods in Context
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For d2ydx2−5dydx+6y=13sin⁡(3x)\frac{d^2y}{dx^2} - 5\frac{dy}{dx} + 6y = 13\sin(3x), what form is assumed for the P.I.?

λsin⁡(3x)+μcos⁡(3x)\lambda \sin(3x) + \mu \cos(3x)

What is the characteristic equation for d2ydx2−5dydx+6y=0\frac{d^2y}{dx^2} - 5\frac{dy}{dx} + 6y = 0?

m2−5m+6=0m^2 - 5m + 6 = 0

If the characteristic equation factors as (m−2)(m−3)=0(m - 2)(m - 3) = 0, what is the C.F.?

Ae2x+Be3xAe^{2x} + Be^{3x}

What is the complete solution to a non-homogeneous S.O.D.E.?

Particular integral + complementary function

For RHS =λekx= \lambda e^{kx}, what P.I. form should be tried?

aekxae^{kx}

For d2ydx2−5dydx+6y=3x2\frac{d^2y}{dx^2} - 5\frac{dy}{dx} + 6y = 3x^2, what P.I. form is assumed?

ax2+bx+cax^2 + bx + c

For d2ydx2−5dydx+6y=e2x\frac{d^2y}{dx^2} - 5\frac{dy}{dx} + 6y = e^{2x} with C.F. Ae2x+Be3xAe^{2x} + Be^{3x}, what form to try?

λxe2x\lambda x e^{2x}

Factorizing m2−5m+6=0m^2 - 5m + 6 = 0 gives which result?

(m−2)(m−3)=0(m - 2)(m - 3) = 0

For RHS equal to constant kk, what P.I. form should be used?

cc

Why doesn't the C.F. alone solve the non-homogeneous equation?

C.F. equals zero for homogeneous equation

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