b) An undamped oscillation under the influence of external : by dr UTM&UTM + kr = dt? %3D O UTM U and spring constant k and let w mas F(t) = Fo cos (wot), where wo # w. What type of value k and m so that the corresponding homogeneous solution is m %3D with external force m UTM UTM UTM an(t) = A cos(wt)+ B sin(wt)? Hence, by using the method of undetermined coefficients, show that AUTM UTM UTM r(t) = A cos(wt) + B sin(wt) + Fo m(w? – wi) cos (wnt).

Q: (1-x)y' = y²

A: Given Differential equation (1-x)y'=y² This can be written: (1-x)dy=y^2dx; separating the variables:…

Q: Compute the differential dy for y = -6x° + 8x5. dy =

A: topic - differential equations

Q: If z= r +y, I= e' cos(s) and y= e' sin(s), then %3D 8z as at (t, s) = (1,0) is O-2e O 4e O 2e? 2e

A:

Q: If f(z, v) – 4z°y+ 8zy, then the total differential of f at z-1 and y - 1is: O df - 17 dz + 22 dy O…

A:

Q: Determine the linearity and solve for the general solution to the given DE * dx ecos y – x cot y dy

A:

Q: u2 and ult) ond Ret) ore both diffrentioble %3D functions. Iff uc8) =3 , K(1) = 2, U'I2) =5,…

A:

Q: O Đ 11) Calculate the Jacobian, J, for the change of variables x = u cos(0) -v sin(e) and y = u…

A: The objective of this question is to calculate the Jacobian of the transformation from the variables…

Q: O Đ 11) Calculate the Jacobian, J, for the change of variables x = u cos(0) -v sin(e) and y = u…

A: The objective of this question is to calculate the Jacobian of the transformation from the variables…

Q: Set w(r, y) = cos(xy) where x = t² and y = el-8t, then dw dt Select one: a.…

A: to find the value dw/dt                   dwdt=dwdx.dxdt+dwdy.dydt                     (1)

Q: Given z = 3x'y + V5 cos 2y-2x, detemine the total differential o

A:

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.