Let the following ODE be x = -2t³ + 12t2 – 20t + 8.5. y(0) = 1 from t = 0 to t = 4 with a step size of h = 0.5 With an initial condition at t = 0 it is X = 1 a) Determine the solution of the ODE b) Determine the solution of the ODE in the given interval

Q: Let u(æ, y, z) = Vr +y + z? where æ = 8re', y = 2te & z = et, du ду dw E Ər ot Әх ду дz Әх or ' or '…

A: Given:      where We have to calculate and  by using the chain rule.

Q: For each first order ODE, state why or why not the ODE is separable, linear, and/or exact (each one…

A:

Q: s) Solve the given ODE y"" + 3y" + 3y + y = e-x-1

A:

Q: x?y" – 7xy' + 15y = x, Yh = C1x³ + c2x³ -

A:

Q: The annihilator operator form for the function e + cos(2x) is:

A: The annihilator operator form for the function ex+cos(2x) .

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.