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Find the general solution to y''+2y'-3y=x

y''=d 2 y/dx 2 , y'=dy/dx for ease of writing First off split the full equation into th homogeneous equation and the particular function. The homogenous equatiion is when our collection of y, y', y'' are on ...
ZG
8685 Views

Find the first three non-zero terms of the Taylor series for f(x) = tan(x).

We have that the Taylor series of a function infinitely differentiable at a x = a is given by the expansion: f( x ) = f( a ) + f'( a )( x - a ) + f''( a )( x - a ) 2 /2! + f'''( a )( x - a ) 3 /3! + f (4) ( ...
AS
13097 Views

The quadratic equation x^2-6x+14=0 has roots alpha and beta. a) Write down the value of alpha+beta and the value of alpha*beta. b) Find a quadratic equation, with integer coefficients which has roots alpha/beta and beta/alpha.

a) We know that, for a general quadratic equation that can be written as : a x 2 +bx+c=0, the sum of its roots (S) is equal to -b/a and the product of its roots (P) is equal to c/a (which can easily be verif...
BC
26740 Views

A useful practice: how to determine the number of solutions of a system of linear equations beforehand

We have a system of n linear equations incorporated by A x = b , with A being a n x p matrix of numeric coefficients, x being a p-dimensional column vector of variables and b being a numeric n-dimensional co...
FB
4223 Views

Find the determinant of a 3x3 matrix.

Will need a whiteboard so I can draw a matrix to fully explain.
SM
3240 Views