tegrating Factor by Formula a.) y²cosxdx + (4 + 5y sin sin

Q: X = acos'0 , y = b sin°0 %3D

A:

Q: The appropriate trigonometric substitution that solves the integral SV5 + 4x – x2 dx - A) x = 2 + 3…

A:

Q: F(x) = 1+e siny x %3D -- = -15 e sin4X- se"co54X fca) = fco) = -8 R fくり) = fci-2) = 4.2398 > KMS %3D…

A:

Q: 1 - / sin2r - ycos2r điferansiyel denkleminin genel çöztumt aşağıdakilerden hangisidir? a) Hiçbiri…

A: Consider the homogeneous differential equation y'sin2x-ycos2x=0. Variable separable form:…

Q: 1. sin'y (2-3 cos y )dy

A: Given: ∫sin3y(2-3cosy)2dy

Q: Homogeneous Find C, if y f(cos 2n) = tan 45° 3(3x + y?)dx-2xydy 0

A:

Q: 1. 2. (D² -3D+2)y=sine-*

A:

Q: 2.x*y" + 2x²y" = x + sin(In x) Cauchy-Euler Find the general solution of the equation.

A:

Q: 2. (sin 0-2r cos 0)dr + r cos 0(2r sin 0 + 1)d0 = 0

A:

Q: 1. x siny + x²y = c 2. xy² – 1 = cy 3. x = A sin(wt + B), w a parameter, not to be eliminated -

A:

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

A:

Q: 3. y" y'-y = cos(5t) - sin(5t); y(0) = 2 and y'=5

A: First find the commentary function then particular integral and then use the initial conditions as…

Q: (x-2) (g-9) 2- 3X+uX- %3D 29-u | Sind general Salantion

A:

Q: (1+sinx)9 cos x dx , u=1+sinx is The values of a. (1+sinx) 10 + C 10 b. (1+sinx)10+ c 1 (sinx)10+c…

A: Solution: The objective is to find the value of the given integral

Q: 10 - f sin(82) arctan(sin 4x) da integralinin değeri aşağıdakilerden hangisidir? a) O T-2 b) - 8 8(T…

A:

Q: (2) Separation of variable c. xcos?ydx + tanydy = 0

A:

Q: sin' y 3 Find the particular solution of xsin?y cos y y' +: 1+In x = 4 :y(e) =

A:

Q: 0 2 1 X' =1 1 -2 X 2 2-1 -cos(1)[C(i+3) +5C,2C, + (3 – 1)C,] + sin()[G(i-1)-5G42G1-1(3-1)0 X(t) =

A:

Q: 1. The value of A. sin-¹(²*²+¹) + C 5 sin-¹(²*x+¹)+C B. C. sin-¹(+¹) + C D. sin-¹ (¹) + C 2x

A:

Q: iii- y +y tan .* sin 2x, y(0) = 1. (Bernoulli Equation) %3D

A:

Q: (c) The displacement, x, of a particle in simple harmonic motion is given by x = cos(3t) – sin(3t).…

A:

Q: Exercise No. 2. Use Elimination of Constants by Isolation of Constants. Show your COMPLETE AND CLEAR…

A:

Q: x'y" + 2x²y" = x +sin (In x) Find the general solution of the Cauchy-Euler equation.

A:

Q: 2.5 1 –dx 1+ sin x – cosx COS X 1

A: Solution

Q: y"+ 25y = 0; yı = y'(0) = -10 = cos 5x, y2 = sin 5x; y(0) = 10, %3D %3D

A: Given differential equation is y''+25y=0 The auxiliary equation is m2+25=0m=±5i Therefore, solution…

Q: sec 2x cos? ydy - (1 – sin y) dæ = 0

A: Given query is to find the solution for differential equation.

Q: 2. The distance between the points (sin x, cos x) and (cos x, -sin x) is: А. 1 В. V2 C. 2 sin x cos…

A: To find the distance between the two points

Q: 3. Find the area of the cardioids region shared by ri 7(1- sin 0) and r2 = 7(1+sin 0). A 7(1 Sint) B…

A: The given curves are:  r1=71-sinθr2=71+sinθ To find the intersecting points,…

Q: -1 cos z sec + C 2 O - sin-l cos z 2 +C 2 tan 1 cos z +C 2

A:

Q: (z*sin - 2° cos 2y cos r2 y? dr+2xy cos ,dy = 0.

A:

Q: x³ + y³ + 3 x² siny tan z = 5 az dz and əx Find ду

A: Given,          x3+y3+3x2sinytanz=5

Q: O 1:0: d (sin-x?) = (sin-1; dx 1 d V1 - x² dr (x²) خيار 4 1 V1- x4 2x V1-x2

A:

Q: 4. What is the form of y, given (D² + 9)y = x + tanx? A. Yp = V,sinx + vzcosx B. Y, = v, sin3x +…

A:

Q: y = cos x, y= sin 2x, x = 0 and x = 2

A: Solution

Q: Cos 4x b. .J dx,u=1+2 sin4x (1+2 sin 4 x )*

A:

Q: 3 Find cos(x+y), given that cosx= and siny = 2 3 TT <y<2n. 0<x< 2 Select one: V5-2/15 a. 10 b. None…

A:

Q: y" + 25 y = 10(cos(5t) – 2 sin(5t)), y(0) =1, y'(0) = 2. %3D %3D

A:

Q: sin z f(2) = cosz Bring your answer to the simplest possible form.

A: Find derivative 4f as per student required

Q: 1. Integrate using an appropriate method. [2si 2 sin³(r) cos² (r)dr

A: The given integral is: I=∫2sin3xcos2xdx   As we know that; The trigonometric identity; sin2x+cos2x=1…

Q: Find a general solution. Show the details of your work [3] yi = y1 + Y2 + 10 cos t y2 = 3y1 – y2 –…

A: See the attachment

Q: Show that y(x) = cos-(Acot x) + B is the general solution to the Euler-Lagrange equation for the…

A: Given function is, ∫1+y'sinx2dx Let, us assume that the function is, Ly',x,y=1+y'sinx2 So, the Euler…

Q: dx If x² – 2x – 4 is solved by trigonometric substitution, the resulting integrand is?

A: The integral function is ∫dxx2-2x-4dx

Q: y" – 2y' + y = [-6x – 8] cos(2.x) + [8x – 11]sin(() 2x) %3D

A: We have to solve the differential equation y''-2y'+y=[-6x-8]cos2x+[8x-11]sin2x.

Q: 8) Prove: Prove that a general solution of the equation y" - y = 0 is given by y = c cosh t+cz…

A:

Q: ∫0π/2[√(cos3x) sin3xdx]

A:

Q: 1. Solve: sin z cos² y dr + cos? r dy = 0, y(0) : (separation of variables)

A:

Q: y = tan x sin (2x)+cos (2x) 2 y' = A sin (Bx) + Ccos(3x) 3. A = B = C =

A: Hey, since there are multiple questions posted, we will answer first question. If you want any…

Q: 9. y"+y= sec² x Ans. y= c, sin x + c2 cos x0 + (sin x ) In(sec x+ tan x)–1

A: Let's find.

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.