Differentiate with respect to t and solve for ds dt s² = x² + y² Step 3 25ds dt ds dt = 2x dx dx dt ds dt + ydy dt X dx + 2y S dy dt dy Substitute x = 120 and y = 160 in s² = x² + y2. (Only positive values need to be considered.)

Q: 7/2012 - y x² + y² (²) di dx + (ye³ +2²) dy = 0

A:

Q: Find dy dx dy dx for y = √u and u = x2 + 3.

A:

Q: Find dy/dx and d²y/dx2 for r = t2 +t +1 and y = t2 + 2t - 1.

A: given that x=t2+t+1 and y=t2+2t-1 we have to find dydx and d2ydx2 Now,          dydx=dydtdxdt…

Q: dy dx Given y=x³ - 2× and = 3. Determine the value of dt when X=2. dt

A: Differentiate the equation y=x3-2x with respect to t. y=x3-2xdydt=3x2dxdt-2dxdt=3x2-2dxdt

Q: what is the dependent variable and linearity of the DE: d(xy)/dx + xy=0?

A: We will find out the required values.

Q: solve the DE using a substitution

A: Given,             dydx=(2x+y-1)3.

Q: P. (F(2³)) dz 13

A: We have to find derivative

Q: Given t = x + ex, find dx/dt

A:

Q: fine the general Solution of 2 Ⓒ dy =secy dx

A:

Q: dy dx 11ey ex

A: dydx=11eyex

Q: dy %3D -9y = 0 with the conditions that x = 0 and dx

A:

Q: Find dx/dt. Since x + y =225, then %3D 2x dx + at 2y.dy =D0 %3D This Simplifies to dx = dt dy %3D

A: Given: x2+y2=225 To Find: dxdt

Q: 3. Population in a town is given by the exponential equation, P = 14000e05st in t years. a. Write…

A:

Q: Find for y=x cott²dt. dy dx 2

A:

Q: Find dy dx dy dx 11 x = √t, y = 4 - t

A:

Q: : Solve-Using D-operator dy dx + 3y – 5x - e-t = 0 dt %3D dt dx dy 2- dt +x +y-3 = 0 dt

A:

Q: dz + et+z = 0 dt

A:

Q: d³r dz +t- dt3 (c) 4tx = 0 %3D dt

A: The solution is given as