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solve the differential equation dy/dx = 6xy^2 given that y = 1 when x = 2

First step is to seperate the variables (EQ1) : (1/y^2) dy = 6x Then we integrate each side seperately giving us (EQ2) : -1/y = 3x^2 + C (remembering to add 1 to the power and divide by the new power) subbin...
DM
Answered by Dylan M. • Maths tutor
10083 Views

How would you determine what sort of stationary point this curve has? x^3 - 6x^2 + 9x - 4

I would differentiate it and then turn it into an equation to find the points where the gradient equals zero. With these points at hand, I would take a second derivative, this tells me how the gradient chang...
WM
Answered by William M. • Maths tutor
6535 Views

(a) Express 9x+11/(2x+3)(x-1) as partial fractions and (b) find the integral of 9x+11/(2x+3)(x-1) with respect to x

(a) 9x+11/(2x+3)(x-1) = A/2x+3 + B/x-1 9x+11 = (x-1)A + (2x+3)B Setting x=1 gives B=4, setting x=-3/2 gives A=1 so the final answer is 1/(2x+3) + 4/(x-1) (b) 1/2ln|2x+3| + 4ln|x-1| + c
AT
Answered by Amelia T. • Maths tutor
5707 Views

Find W where: 11-W/4 = 1+W

11-W/4 = 1+W 11-W = 4+4W (Multiply both sides by 4) 11 = 4+5W (Add W to both sides) 7 = 5W ( Subtract 4 from both sides) W = 7/5 (Divide both sides by 5 to get your final answer)
LW
Answered by Liam W. • Maths tutor
10814 Views

Find the derivative and following function and hence find the value of coordinates for when the function is at a stationary point:

y = e x x 2 + e x : The derivative can be found using the chain rule. (A reminder of the chain rule: if y is a product of two functions of x i.e if y = F(x)G(x) , the derivative is as follows: y I = F I (x)G...
MC
Answered by Michael C. • Maths tutor
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