Solve the following initial value problem: Cos(t)² dy 1 dt

Q: The equation implicitly defines as a function of t. Find dat dx || t² z2 -sin (9 x) = -4

A: The given equation is -t2x2-sin(9x)=-4 To find the dxdt.

Q: Given the equation p=2x/y, find dy/dt

A: Using the properties of the logarithmic functions, it can be written that lnab=ln a-ln b. It is…

Q: find dy>dt.…

A: Given that y=1+cott2-2.

Q: Determine the derivative dy da for each of the following equations.

A: (a) y=log8⁡(4)

Q: Find the derivative of y with respect to t. 3. 0<t< 2 y = sec 2t3 dy dt

A:

Q: dx

A:

Q: The equation implicitly defines as a function of t. Find dr dt da dt 11 2 cos (6 x) = -8

A:

Q: Find dy/dt. 13) y = (1 + sin 12t)-3

A: Given, y=1+sin 12t-3

Q: d Find the value of f(x) if f(x) : cos (t) dt. dx. COS f(x) =

A:

Q: 3x 9. Find *(t² - t) dt. d dx '3

A:

Q: Find the general solution to the linear ODE. Use each method (integrating factors and educated…

A:

Q: Q2/ solve the following differential equatio dx 1. = x + xy2 dt

A:

Q: Find the following derivative and state a corresponding integration formula. 4x - 6 dx x2+2x-5 da…

A:

Q: A. Find the function f that satisfies the equation / f(1) dt : 2 cos x + 3x – 5. d B. Evaluate: dx 3…

A:

Q: Determine which of the following equations is linear and which is nonlinear; give reasons: dx dt…

A: We have to identify which of the following differential equation  is linear and which one is non…

Q: Use a substitution to find the implicit solution to the equation dy dt tan(t + y)

A: Given differential equation:To find:Solution of  using substitution method

Q: Find the following derivative and state a corresponding integration formula. 3x - 1 2x2 + 2x + 2 d…

A: Derivative

Q: dy + (3 tan(3t))y = cos(3t) subject to the condition that cos(3t) > 0. dt

A: To Find:Solve the above equation subject to the condition that .

Q: If y = (tan(x³) + 6)6, then dy equals dt

A:

Q: B. Solve the following problems using differen linear approximations. Show complete soluti 2.…

A: Sol

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.