Specify it if the differetial equation is exact or non-exact. FInd the general solution. 2ydy = (3y^2 cotx = sinxcosx)dx

Q: «) sin3x sinlx dY

A: See the details solution in below

Q: 3. J sinh(5x – 1) dx

A: Please refer the attached image for complete solution.

Q: S sin³xdx =

A: Here we have to solve the given Integral.

Q: Iim tan³x X10 1- Cos2x

A:

Q: السؤال 3 -Sec2 (). dx tan (5). · dz O ). de tan tan . da O ). dz O tan

A:

Q: ( sinh3x cosh³x dx

A: Consider the integration as I=∫sinh3xcosh3xdx

Q: Integrate the square root of (1 - sin² x) dx.

A:

Q: 3.§ sin* 2 x sin 4 xdx

A:

Q: C.)+x) = sin2x -tonzx

A:

Q: Find [(x- sin(2x)) dx

A:

Q: find the most general antiderivative or indefiniteintegral. You may need to try a solution and then…

A: ∫3t2+t2dt⇒∫3t2+t2dt=∫3t2+dt+∫t2dt                       =3∫t2dt+12∫t dt…

Q: Period of y = sin 3x

A: Given, y=sin(3x) ∴ Frequency in radians, ω=3 ∴ Frequency in Hz, f = ω2π => f = 32π Time period, T…

Q: Integrate dx/(sinx+cosx)

A:

Q: csc squared x/2 = 2/1-cosx verify with steps

A: To Verify:

Q: olve the equation on the interval 0s0<2x V2 sin0- sin 0 = 0

A:

Q: coshx 5) dx ++sinh²x

A: Some of the important formulas  d(sinh x)dx=cosh x ∫1a2+x2 dx=ln x+a2+x2 +C

Q: 3. dx (sinh(2xV1+x du

A:

Q: 3- Sin4x dx S 3-Sin4x dx ノo

A:

Q: Solve S(cosa{x – +)<(1 + +) dx -

A:

Q: Solve: cosx + sin x + 1 = 0, 0 sxs 27.

A: Given: cos2 x+sin x+1=0, 0≤x≤2π

Q: ( 2sinx sin(2x) dx

A: Given,        ∫2sin2xsin(2x)dx

Q: | sin³(18x) dx =

A:

Q: Solve the equation for x  arcsin√2x = arccos√x

A: The given equation is sin-12x=cos-1x

Q: 2- Solve the equation for x : Cosh x = Sinh x +1/2.

A: We need to find out the value of x. The given equation is Cosh x=Sinh x+12 Now,  Cosh x=ex+e-x2  and…

Q: sin3x dx 1+ tanx

A:

Q: Evaluate the following integral sec(/T) tan(VT) dx

A: The given integral,      ∫secx tanx dx

Q: Calculate. -dx 3-2x

A:

Q: dx 20.5 x√4x²-49

A:

Q: 1- 1- (Sin (coshx) sinhx dx

A:

Q: find the largest and smallest value of the function y = 3-sin3x

A:

Q: ) Evaluate cosx sinx V1 – sin4x dx.

A: Use substitution method to solve this

Q: 2. (sinhx+ coshx)*

A:

Q: cos(2x-1) dx (Integratio

A:

Q: +2 dy x2 + sinx – y = 0 dx

A:

Q: Evaluate : e2x sin3x dx

A: Introduction :

Q: S sin2xsecx dx

A: LetI=∫0πsin2xsecxdxI=∫0π2sin2xsecxdx+∫π2πsin2xsecxdxWe know that sin(2x)=2sin(x).cos(x)I=∫0π2secx·…

Q: Find the root of the equation Cosx-x' = 0 near to 0.5 using Newton-Raphson method correct up to 3…

A: To determine the root of an equation using Newton-Raphson method, first choose an initial value x0…

Q: Evaluate the intergrals. ∫ ex sin2x dx   show the complete solution. step by step

A: There are exponential function and trigonometric functions in the product in the given integrand.…

Q: Evaluate the intergrals. ∫ ex sin2x dx

A: Given: Let I=∫ex sin 2x dx To Find: To evaluate the given integration.

Q: S sin5xsinx dx

A: Integrations are generally used to find area under the curve when the limits of the integral are…

Q: Find Dx (sin4 x).

A: we have to find the value of Dxsin4x

Q: Solve to find general solution: dy = Exe xez -1 1-x²y dx

A:

Q: X= sin 2tS In %3D Find dw 2- Cost

A:

Q: sin (2x)dz

A: Given ∫e6xsin2xdx

Q: 6 sinx (cosx + 1)5 dx

A: We will find the value of definite integral as following.

Q: 6x 4. se eo* sine³x dx ‚3x

A:

Q: Differentiate y= x2  sinx

A:

Q: 9 coshx - 5 sinhx 15 %3D

A: To solve  9coshx-5sinhx=15

Q: S sin32x dx

A: To evaluate the integral: ∫sin32xdx Solution: Rewriting the given integrand. ∫sin32xdx=∫sin22x…