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Solve the following ordinary differential equation:

(a) dy/dx=(y-x)/(x-4y)

(b) (2yx^2+4)dy/dx + (2y^2x-3)=0

(c) y"+3y'-10y=3x^2

(a) dy/dx=(y-x)/(x-4y)

(b) (2yx^2+4)dy/dx + (2y^2x-3)=0

(c) y"+3y'-10y=3x^2

Identify the following differential equations and hence solve them

1) y'=-4/x^2 -y/x +y^2

2) y= xy'+1- ln y'

1) y'=-4/x^2 -y/x +y^2

2) y= xy'+1- ln y'

The linear equation y = 4x + 90 can be used to calculate the total cost y (in pounds) for x teenagers attending if they choose the cinema. Explain why this equation holds

(2yx^2 +4)dy/dx+(2y^2x -3)=0

dy/dx=(y-x)/(x-4y)

find the complete integral of the equation (dz/dx1)(dz/dx2)(dz/dx3)= (z^3 X1 X2 X3)

A tightly stretched string with fixed end points x=0 and x=1 is initialy in a position given by y=y0 sin^3(pi.x/l). it is released from rest from the initial position. find the displacement y(x,t)

Do the functions y1(t)=root t and y2(t)=1/t form a fundamental set of solutions of the equation 2t^2 y'' +3t y' -y=0, on the interval 0 less t less ~? justify your answer.

A certain population is known to be growing at a rate given by the logistic equation dx/dt=x(b-ax) show that the minimum rate of growth will occure when the population is equal to half the equilibrium size, that is when the population is b/2a.

Solve the differential Equation

d^2y/dx^2 +3dy/dx -10y=3x^2

d^2y/dx^2 +3dy/dx -10y=3x^2