Consider an ODE of the form dy dy + 2p(x) + (p(x)² + p'(x))y = q(x). dx² dx If I = exp(ſ p(x)dx) is an integrating factor, show that the ODE may be written in a simpler form, d (Iy) = Iq(x).

Q: Consider the function f(x) whose second derivative is f''(x) = 3x +4 sin(a %3D If f(0) = 3 and f'(0)…

A:

Q: Find y' y= (x2+2)(x-3)

A: Given :                  y = x2+2x-3 Find :               y'

Q: A function y = f(x) with the property that y = y'= y" is %3D

A:

Q: The derivative of f(x) = 5x – Vx + (sin)x – e² -

A: Given; f(x)=5x4-x1/3+[sin(π/2)]x-e2

Q: Use the chain rule to find the derivative of 13 f(x) = 3(6x* – 5a³)* You do not need to expand out…

A: Given that:f(x)=36x4-5x313To find f'(x)

Q: 3 X 1 2 3 4 5 f'(x) 5 12 4 3 g'(x) 3 245 1 [3f(x) - 4x] x=3 =(Type an integer or a decimal.) www

A: We will find the required.

Q: Find the first derivative of the function g(x) = V5 +x +4cos (2x).

A: The function f(x) is a rule that associates or fixes a number to the particular point x. If y=f(x),…

Q: In f(x) dx = F(x). F(x) is called the

A: follow the procedure given below.

Q: Find the derivative of F(x) = 4 sin(t) dt. 3x %3D dx cos(x)

A: Solve the following

Q: Find dy/dx if f(x) = csc (x³ + x + 1)

A: Derivative of the function

Q: The y' for y = (x³ +

A:

Q: Let f(x)=100/5+2e-0.01x. Find f'(x).

A: Write the given function using exponent.

Q: a) If f (x) = 12x, find f' (27). %3D

A: Solve the function

Q: If f(x) = 18z + 9, find f'( – 1).

A:

Q: If f(x) = 6(sin(x))ª, find ƒ'(3).

A:

Q: Find f'(0) if f (x) = In(cos .x).

A: we have to find f'(0)

Q: S(x)= cos' ( (2x)). -cos? sın Show that f'(x) =-6 cos" (sin(2x)) sin (sin (2x))cos(2x).

A: Given, the function f(x)=cos3sin2x. Then we have to show that f'(x)=-6cos2sin2xsinsin2xcos2x.

Q: Suppose F(8) = 5, F(9)= -23, and - 9 f6f (x) d Your Answer: Answer dx= F'(x) = f(x).

A:

Q: Find f. (x + 1) f'(x) = (1) = 3 %3D f(x) =

A:

Q: Differentiate the given function. 7x-2+-

A: Here we apply product rule of differentiation (UV)' = U(V') +(U')V

Q: Let f(x) = 9 + V2x - 9. Find f(r).

A:

Q: F(x) = Vt² + 11 dt

A: F(x)=∫5xt2+11 dt

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.