1. Solve the following DE using Variation of Parameters: (D2 + 1) y = secx tanx

Q: 3. Find y': y = 5sin3x

A: The given function is, y=5sin3x We need to find the derivative of the given function. The derivative…

Q: y = sech 0 (1- In sech 0)

A:

Q: x2+1 - dx x4-x²+1

A:

Q: Sx sech2 x² dx

A: Given:  Integral of xsech2x2

Q: Find Y = Coth 1 (x)

A: Given that y=coth-1x find dydx

Q: Find an equation of the line tangent to the graph of y sin x – 3y = 4 at the point %3D (, 4) .

A: y2sinx - 3y = 4 at (π/2 , 4) we have to find slope of function 2ysinx(dy/dx) + y2cosx -3dy/dx = 4…

Q: Solve: y (cosx)= (9+ y²)

A:

Q: Give nonlinear equation:

A: Given,             sinx=cotx and x0=1, and x1=0.5

Q: (23×e¬*)dx

A:

Q: 3. tan x dx

A: Formula: tan2x=sec2x-1

Q: find the Joriative Y= 3x° seccx)

A: Here we find the derivatives of given function.

Q: Find sec 0. ? (7, V15)

A:

Q: 5. (x2 - y?)dx – 2xydy = 0 %3D

A:

Q: Solve for y. x= (3y+5)/(7y-1)

A: To solve for .

Q: dr Find if r (x) = 9x 2 + 5x – 3. dx

A: Given,            r(x) = 9x2 + 5x - 3

Q: T= tan (x+2y+ 3Z) %3D Find: Txx XX Tx Txy Ty Tyy Tyx Tz Tzz Tzx T zy

A:

Q: y = e² -Vx sec 6x 3

A:

Q: sec2 ) 15. Evaluate. - x2 dx

A:

Q: 1. Solve for 'x': vx + v2x +7 = 8

A:

Q: Q.2: Evaluate: -2 2 dx 1 I = x2 - 8.

A:

Q: nd / (2x° + 7x°) dx

A: