S 1 C=S²x + Sin'x

Q: y'tan x sin 2y = sin² x + cos² y.

A: We need to solve y' tanx sin2y=sin2x+cos2y This can be written as: y' tanx…

Q: Find y" by implicit differentiation. x² + 5y2 = 5 %3D

A:

Q: sin (Vx).cos (Vx) dx = ?

A:

Q: 6. sec (sin-1 x)

A: Interconversion

Q: | sin'x-cos'x dx

A:

Q: d csc 'x dx -1 Prove that xVx? – 1 2.

A:

Q: 2. 2 | sin xcos xdx

A:

Q: Find all complementary functions of the equation xy" - 2y'=0, x>0 1, x² x₁ x³ a. b. C. d. x, x(Inx)²…

A:

Q: d Verify tanh - = X 1- x2 dx

A: Inverse hyperbolic tangent function can be expressed in logarithm funtion. Write tanh-1x=12ln1+x1-x…

Q: (a) [- 9x2 +x° cos x dx = 3

A: Since you have asked multiple questions in single request  so we  will be answering only first…

Q: solve    y'''-y' = cosx

A: Given:       y'''-y'=cosx    Linear equation with constant coefficients…

Q: If f(x) = 5 sin(x) + 3 9x4-3 ƒ'(x) = then:

A:

Q: cosx + cosxcot’x secx

A:

Q: 1- x Vx2 + 9 dx. 1 2-5 dx 1+ sinx 3- sin'x cos'x dx

A:

Q: Find h' (x) if h(x) = sin (2e).

A:

Q: cos(4x) cos(2x) sin(4x) sec(2x) 12. Verify: - sin(2x)

A: cos(2x ) =cos2(x)-sin2(x) = 2cos2(x)-1 =1-2sin2(x) sin(2x) = 2sin(x) cos(x)

Q: Using Variation of Parameters 4y''-4=cos-1x

A: Given that, 4y''-4=cos-1x Now let's take, 4y''-4=0 Take m=ddx, 4m2-4y=04m2-4=0m=±1 So the homogenous…

Q: S (|sin x| + sin æ') dx

A:

Q: 1. sin° x cos x dx

A: sin3x cos4x  = sin(x) sin2(x) cos4(x)  = sin(x) (1 - cos2(x)) cos4(x)  = sin(x) (cos4(x) - cos6(x))…

Q: 3 sin x 1. S- dx 1+cosx

A:

Q: Find the y'(0) when y = cos (sec²(2x))

A:

Q: 8e cos 2x dx csc(x) sec(x)

A:

Q: | sin´x-cos²x dx

A:

Q: 7 (1 + sin² x) = e 2" sin 2.x, y(0) = 1 X 7) dx

A: This equation solve by separation variable

Q: 1 [In(3x)] S (* -5x+2)e*dx

A: solution is given below