2/solve the differentialequation by using methad af Variation of (complete salution is vequired) parameters. f(x) take F(x) = Cos 11 X

Q: If f(x) = 5x(sin x + cos a), find f'(x) = f'(3) =

A:

Q: (7) coshx + sinh x = e* %3D

A:

Q: Derive y = e*+1 sin x³,

A: To find the derivative of the given function we use product rule of differentiation,  chain rule of…

Q: e. f. f(x) = cot(-) X f(x) = sin(x³ - x)

A:

Q: Q3: Find the first derivative of y= cos(x) at x= t/2 using a step size of h= Tt/12. Use forward and…

A:

Q: Solve Sin (3x) %3D cos (2x)

A: to find derivative of y=sin3xcos2x

Q: Find the second derivative of the following function at x = 2 y = (x +) 2 G+x)

A: Given function is y=x+1x2

Q: If C(x)=x' + x°, evaluate the fourth derivative at x = 2. %3D

A: To find the fourth derivative of the function: C(x)=x5+x-3 at x=2

Q: Let xy2 - x = y; Use implicit derivative, find y' O (3x? - y?)/(2xy-1) O (3x - y)/(2xy-1) O (3x2 -…

A: Explanation of the answer is as follows

Q: x²Sin(x) y = In 2x + 1 9.

A:

Q: Ex6: Solve the following 1. If x? + y² = 25 show that (y')² + yy" + 1 = 0 2. If xy = sin x show that…

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: 1. f'(x) = cosx and f(0) = 5, find f(x).

A:

Q: Q2\Find T.E of the function f (x) = sin 2x when a =1?

A: Given that  f(x)=sin(2x) at a=1  To find the T.E

Q: 1. L 16x dx 2. o &. + 2 +1 3. (sec x- tan x dx dx 4. cos x tan x 1/4

A:

Q: Use backward-difference formula to evaluate the first derivative of y = ³-4 at x = 0 using a value…

A:

Q: 13 If f(x) = t? dt then %3D f'(x) = %3D

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.