d^2y/dx^2 + 3dy/dx + 4y = 3x + 2 Utilize the indeterminate coefficient technique to solve the above equation

Q: dy + sin 2x + sin 2y + 2 sin 2x sin 2y dx solve by Separable method

A:

Q: = - 1) ex²-x dx x. Use the substitution method to rewrite the function in the integrand, (18x – 1)…

A:

Q: Find sec42x -dx tan 2x A --—-—-cot²2x-—-—-cot³21+ C 16 cot82x) (4sec22x-1) B -(cort2x) 4 12 11 1 C)…

A:

Q: Iim tan³x X10 1- Cos2x

A:

Q: Find sec 2x -dx. tan 2x cot82x (4sec 22x-1) (A) 12 1 1 I B 12 tan 2x 16 tan 82x Ⓒ -co1²2x-co1³21+ C…

A: Here is the solution

Q: COS V4- x2 dx -2 1/2

A:

Q: (x-7) dx 19. SJ5-4x-x2

A: Answer is following.

Q: sin(2t +) dt eu-3 %3D 64

A: Let, I =∫0∞sin2t+π2e2t-3dtApply integration by part ,Ist function = cos(2t) , since sin(π/2+x) =…

Q: sec2 (을) dx 23

A: The given integral is ∫sec24x2x3dx.

Q: Solve - s d²y + 6y = 2 sin 4x dx | %3D .2

A:

Q: 2 Solve equation (D² +1)y-secx tan x using method of variation of parameters. %3D

A:

Q: Solve the integral. 6х — 3 1.5 -dx 4x2 – 4x + 1

A:

Q: y = sin(3 – 4x)" %3D

A: Apply the chain rule of derivatives, If y = f(g(x)), thendydx=d(f(g(x))d(g(x))×d(g(x))dx

Q: Solve f 4x cos(3x) dx using Integration by Parts.

A: This is based on integration by parts

Q: Integrate √2 2 | sin x 2 √1-x² dx

A:

Q: 5tan 2x -dx- sin22x-1 8.

A:

Q: y = 2 sin 3x 1+3cos2x

A: We are given  y= 2sin3x/(1+3cos2x)  We have to compute y'.    Before computing y', let us first see…

Q: π/2 sin3 (4 ) αθ - π/2

A: To evaluate the following integrals

Q: 5sin(4x + )sin(2x-)dx

A: The given integral is, The integral cannot be solved directly and we would have to use some…

Q: Integrate: - da 9x2+16 O In (3x + v9x2 +16) + C O In (3x + V9x2 +16) +C ㅇ tan ' (뚜) + C 0 tan1 (부) +…

A: Given ∫dx9x2+16

Q: 2x+5 dx = AV7- 6x - x2 + B sin - (**)- 1. Vア-6xーx2 +C

A: ∫2x+57-6x-x2

Q: csch (2 sin2x)dx 1. 1– 4x²

A:

Q: Complete the integration: 1 1 Scos (2x)dx = sin 2x -sin 2x + C Determine the value of "?".

A:

Q: (T/3 4 sinx -dx 1-4cosx 1-

A: As per our guidelines we are supposed to answer only one question. Kindly repost other question as…

Q: solve using variation of parameters or reduction of order. (D2 + 1) y = tan x

A: Given (D2 + 1) y = tan x

Q: Solve (D² - 2D + 5) y = sin (2x) + 17x cos (2x) — 15x -

A:

Q: (D² – 3D+2)y= sin3x

A: We will find out the required general solution.

Q: sec(tan(2x)) – 4 6. dx (cos(2x))? 8. / e*-* dx T e3x-e3x

A:

Q: 1. Ssin (2x-1)cos (2x-1)dx

A: 1) Evaluate: ∫sin42x-1cos32x-1dx

Q: Solve sin - () 2 dy = x + y

A: We need to use substitution method to solve this differential equation

Q: ( csch (2 sin 2x) dx V1-4x

A: We have to find indefinite integral

Q: -r°(1-cos2x) 1- dx 2

A: 1). To evaluate the integral: ∫π01-cos2x2dx Solution: Evaluating the given integral.…

Q: .2 x² arctan(3x) dx %3D

A:

Q: y = sin(2x – 27)+1

A:

Q: 5. y = tan 5x %3D

A: Given that y = tan5x sketch the graph. Here i attached solution of this question.

Q: 1. D² {Sin ² x 3 2. JD²-15² √2e²x3

A: Here D is the differential operator. D=d/dx

Q: what is the integration of x^2/(9-x^2)^3/2 using trigonometric substitution

A:

Q: 3 y = sin³ 2x

A: We have to use chain rule here.

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

A:

Q: Solve 3x^2-Siny=0, xy^2-x^3+7=0, initial point (-1,2) .

A:

Q: Evaluate the integrals

A: Given integral, ∫π23π41-sin2x dx

Q: Solve (sin23x)dy= dx cot3x + C 3 cot3x O b. y= 3 sec3x O C. y = O d. y = sec3x + C 3

A:

Q: 1. gx-) = - โ -เ sin 2x X< L2x

A: Given: gx-π=0x&lt;π12sin2xx≥π To find: Solution

Q: 2. Solve the DE: -+secx(y-2sec³x+2 sec² x tan x) + y cotx=0 dx

A:

Q: 2cosx dx 2 1+(sinx)²

A: Please refer the attached image for complete solution.

Q: Solve f 8x cos(7x) dx using Integration by Parts.

A:

Q: 3x dx | sec 2

A:

Q: (ii) sec2 (x) dx

A:

Q: 5- y = 1+sin(4x2 + 2)

A: Note - As per our guidelines we will solve first question only and rest will reposted.  ddxxn =nxn-1…