3. Evaluate [2(sin? x+ cos x) dx is Solution:

Q: (D² – 5D + 6)y = 15 sin x – 15 cos x - -

A:

Q: y"+4y' + 3y = sin e*

A: Solving the differential equation by variation of parameters method

Q: Differentiate y= e*cos (x²): y = A e(cos(x?) – 2xsin(x?)) B -2xe"sin(x?) (c) e*cos(x²) – 2 xsin(x²)…

A:

Q: 1. y = x' sin? (2x2) 2. y = In (sec? e) 3. У%3D 1 xe4x 16

A: Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: -п/2 сп/2 w L cos dz dy de (ху

A:

Q: 3 cos (x) sin (x) dx = %3D 2 15 O None 6

A: To find the value of given ∫0π23cos2xsin3xdx

Q: Obtain the general solution of the following equations: sin y(x+sin y)dx+2x2cos ydy=0

A:

Q: The integral / 2/ (*) cos(2*) dx takes the form k cosu du when u=2* and f (x) =x – 5. what is the…

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Q: Find the general solution of tan x dx + y cos? x dy = 0.

A: Use seperation of Variables.

Q: Find a particular solution to y" + 36y = 24 sin(6t). %3D

A:

Q: (10) The result of (D-3D D, +2D;)sin(x-2y) is

A:

Q: tanr sec r dx 3

A: Here we will find the antidarive.

Q: Find the general solution of cos x dy + (y sin x – 1) dx = 0

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Q: 5. Derive the general solution of x cos? y dx + tan y dy = 0

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Q: Given the following DE (cos 2y – 3x?y?)dx + (cos 2y – 2x sin 2y – 2xy)dy = 0 -

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Q: /2 (e) [™¹², sin(x) cos(x)dx

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Q: The solution to the equation is * y'(x)- 2y'(x)+ y(x)-cos(x) slad Ja sin(x) - y(x) =c,e" +e,xe"…

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Q: dy 29 + y tan x: dx 1 (4x + 5)? y³ cos x

A:

Q: Determine the General Solution of sin x sin y dx + cos x cos y dy = 0.

A: Given differential equation is sin x sin y dx+cos x cos y dy=0

Q: dy The general solution of the DE cos?y is dx A y=tanx + C y=tan-(x) + C у-cos"(x) + с D y= sec?x +…

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Q: y(x) =- 10 n +2x' +8x' + 48) +qe* +c, sin(x)+ c, cos(x)

A:

Q: If ſ x sin x cos x dx = xsin²x + Ax + B sin 2x + C, what is the value of A + B?

A: The given integral is, ∫xsinxcosxdx=12∫x(2sinxcosx)dx=12∫xsin2xdx=12∫xsin2xdx=12I1

Q: If dy/dx=sin(x)cos2(x)dx and y(pi/2)=0, whats the value of y(0)?

A: I am going to solve the given problem by integrating the given differential and by substituting the…

Q: B-The result of dy/dx for the following function is cos x y = 1+sin x

A: We have to find out derivative

Q: 2. The antiderivative of cos Π.Χ. A. -cos 2 B. KIN COS C. sin D. sin π.χ. is

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Q: B-The result of dy/dx for the following function is COS X y 1+sin x

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Q: ind the solution of with y(0) 2 and y/(0) = 5. = = y" + 4y = 96 sin(4t) + 96 cos(4t)

A:

Q: Scos(ex).cos"x dx

A: ∫cos3x.cos2x dx=∫cos(5x)+ 3(cos(3x) + cos(x)) +cosx8dx= 18∫cos5x dx + 38∫cos3x dx + 12∫cosx dx=…

Q: 2:Solve: cos (x+ y) dy = dx %3D

A:

Q: 2n 37 So² S67 (x sin(y) – y cos(x)) dxdy = %3D

A: The given question can be solved as shown in step 2.

Q: LE (4y°x² + Sin 2x + Cos²3y) dy dx

A: we have I = ∫-11∫-2-1(4y3x2 + Sin 2x + Cos23y)dy dxlets slove each term separatelyI1 =∫-11∫-2-14y3x2…

Q: Find the general solution of y(4) + y" = 3t2 + 4 sin t – 2 cos t

A: Given differential equation is y(4) + y" = 3t2 + 4sin(t) - 2cos(t)

Q: cos 2y dy sin y

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Q: 11. sin(x) + cos(y) = ey

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Q: et cos(e') dt = (b) +C 3+4 sin(et) 3/4 sin-1 (c) (승교) dx = 16x?

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Q: Find the solution of sin 3ædx + 2ycos³3xdy = 0 O y? = sec 3xtan 3x + C O y? = -sec 3ætan 3x + C O y?…

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Q: 7. y" + y = 3 sin(2r) +t cos(2t)

A: The general solution of an ordinary differential equation of the form;…

Q: T/2 ( 4 cos (x) sin° (x) dx

A: To evaluate the integral ∫0π24 cos2(x)sin3(x) dx We know that, cos2(x)=1+cos2x2sin3(x)=3sinx-sin3x4…

Q: S 4 cos (x) sin (x) dx = %3D

A:

Q: Solve the given problem below: (2x + y cos x) dx +sinx dy=0

A: We will solve it by exact differential equations method.

Q: d dx et ex sin x + e* cos x

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Q: (c) So cos(-x)(x²)dx (d) S(3x² – 2x + 1)sin dx

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Q: Find the solution where y= 1 and dy/dx = 0 when x =0 and describe the behaviour of the solution for…

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Q: Q: Evaluate : fe 1- cos 2ax dx. 1+ sin 2 ax 2ax

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Q: 1. Evaluate 9/ COS x (a) (1 – x)e dx (b) ,"™ dx p) A-2 sin r -

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Q: Find the general solution of the DE: dy/dx = sin(7x) cos(5x) + cos(7x) sin(5x).

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Q: B) Find and It x sin 3z and y= tan 3z dx

A: x=sin23xy=tan 3xWe need to find dydx and d2ydx2.

Q: Find the complete solution of the DE D´ (D– 1)y = 3e* +sin x.

A:

Q: D. ( [ 3° cos"(5t) dt sin(z)

A: