Which is an appropriate trial form for the non-homogeneous equation y/" + 2y' + 5y = e' cos(2t) (a) yp(t) = Ate sin(2t) + Bte' cos(2t). (b) yp(t) = Ae cos(2t). (c) yp(t) = Ate* cos(2t). (d) yp(t) = Ae sin(2t) + Beʻ cos(2t). %3D %3D

Q: JO (5) Find the derivatives (a) d # t ( * cos(2³) dz + 35e) 4

A: Since you have posted multiple questions i can do first question as per our company guidelines.…

Q: (10) y = एस COS (5x) ) y' = ?

A: By applying the product rule for the differentiation.

Q: ch of the following is the result of differentiating both sides of the ation x sin(y)=In(x)+y² with…

A:

Q: Find y'' if y=-6 cos x. OA. y' = 6 sin x OB. y' = 6 cos x OC. y'= -6 cos x OD. y'= -6 sin x

A: The function is given byTo determine: The expression of the second derivative of the function.Formul…

Q: 6. y cos5 (sin(2x)), y'=?

A:

Q: Show that the solution of the differential equation dy/dx=sin(x+y)+cos(x+y) is  1+tan(x+y)/ 2 =…

A:

Q: Find F '(x). F'(x) = F(x) = 14 3 √ sin(x) 7 √t dt 0 -sin 3 2 dt

A:

Q: 7. Find y'if y=x³+ sin (x)

A: given

Q: Find the general solution of the following differential equation: a) t * dy/dt = (1-y^(2))^(1/2).…

A:

Q: y'' - 15y' + 60y = e^x cos(16x

A:

Q: If f(x) = e2" [sin(=)]°, what is f'(x)?

A:

Q: y''' + y'' = cos(2t) y(0) = 1, y'(0) = 2, y''(0) = 3

A: See the details solution in below

Q: If f(x)=√x+3, g(x)=x², then (fog)(x) = The differential of the function f(x)=tan(cos.x) is_ The…

A: We know that derivative of d(cosx)/dx = -sinx. And d(tanx)/dx = sec2x. And derivatives power rule is…

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.