Differential Equations Answers

Find the Taylors expansion of f(x) = Sin x at x = 0

Taylors expansion of f(x) = Sin x at x = 0.

Suppose tank A contain of 500 liter brine wit initially 500gm salt dissolved in it,whereas in tank B containing 500liter of water with initially 250gm salt dissolved in it.Water allowed to enter tank A at a rate of 30liter/minute,and that mixed solution flow from tank A to tank B at a rate of 40liter/minute.At the same time,10liter/minute were pumped back from tank B to tank A,while the mixed solution also is drained from tank B at rate of 30liter/minute.Let's x and y represent the amount of salt in tank A and tank B respectively at any time,t,so the rate of change of the amount of salt in each tank can be formulated as following system :
dx/dt=-4/50 x+1/50 y
dy/dt=4/50 x-4/50 y

What is the scale factor from a to b

Solve the system of differential equations dy/dx =xz+1, dz/dx =-xy for x=0.3 using 4th order R-K method with y(0)=0, z(0)=1.

Solve DE r^2 +4r+3=12

We have a curve passing through (1,2) has the property that the length of the perpendicular drawn from the origin to the normal at any point of the curve is always equal numerically to the ordinate of the point. Please find its equation.

If y = cosx.sinx, differentiate with respect to x.

If GC: 5 and GE: 7 and FC: x and FD : x+ 5 and AD: 7 find the value of x