Test the DE for exactness then solve. 6. (2xy³ + cos x tan y + 2 sin x) dx + (3x²y² + sin x sec? y – 3 cscy cot y)dy = 0

Q: Solve the following Exact DE using Method of Grouping. 2) (y sec?x + sec x tan x)dx + (tan x + 2y)dy…

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Q: Q2- (75 %): Classify and Solve; d?y dy cos? t + cosht + sinh t + sin? t +3 sin t - 3t + 9 %3D dt2 dt

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Q: 1.) Which of the following is not a solution to Show your solution. a.) y = xcos(x) + kx b.) y =…

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Q: 2. Solve for y in terms of X for the following equations: a) In(1- 2y) = x b) In(y- 1)- In 2 = x +…

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Q: 6. Find the general solution: sinx sec? x cos? y dx+ dy = 0 a. secx + tan y = c b. 2 tan x + sin² y…

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

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Q: Solve the following DE using separating of variables method. Giving your answer .in the explicit…

A: After separating the variables to one side of the equation,we will need to integrate using by-parts…

Q: The approximation of I = S, cos x? dx using composite Simpson's rule with n 3 is: -1.5412 O This…

A: Formula :     The formula for composite simpson's rule is     ∫abf(x) dx ≈∆x3 [fx0 +4 fx1+2fx2+4…

Q: 7. Find the general solution: ydx + (1 +x?) arctan x dy = 0 a. secx – tan y = c b. arctanx + sin y =…

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Q: 4 .Using n=8 approximate the value of cos(1+Vx )dx using 0. (a) the Midpoint Rule, (b) the Trapezoid…

A: Formula used: Midpoint rule- The interval [a,b] into n subintervals of equal width,…

Q: Show if the following statement is true or false. If it is true, write TRUE. If it is false, write…

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Q: (b) S¤(tan? #)dx (c) S cos(2t)e'dt (d*) S(arccos x)²dx (e*) S (1+ 3x)2 dx Hint: Check for a similar…

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Q: 0Z for the function : a x Find x2 sin ( y ) + x e cos ( z? ) = 3 y - 6 z + 8

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Q: 5. Let y (sin(2r)) (nz). Find 2. Express your answer only in terms of r.

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Q: Solve the equation for x, where x is restricted to the given interval. y = 4 cot , for x in (0, 2x)…

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Q: Consider y@) + y" = 1+ cos( - t) Then a suit- able form of the particular solution can be written as…

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Q: Given: (2xsinycosy-x+2x2eyx^2)dy=(y-sin2y-4xyeyx^2)dx Show the complete and detailed solution of…

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Q: (x cos + y sin?)y – (vsin? -x cos?)* х — х COS = 0 Ans: xy cos = c (Lucknow, 1997; Kanpur, 1996)

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Q: 11. Given: √√√-x² + 4x +5 dx. Using trigonometric substitution, what is the integral form in terms…

A: The given integral is: I=∫-x2+4x+5dx That can be written as:…

Q: /4 sec? Vwdw a) b) sin 2.xcos xdx c) f tanh xdx

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Q: Consider (D² +1)y = sin²x_ Using variation of parameters, what is the form of y ,? А y =f cos x + g…

A: As per guideline we have to solve one question Please repost other question again

Q: dy 1-5e + y cot x 5e", with y(z/2) =-4. Cos 7) %3D Ans.: y = dx sin x

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Q: 6. Find the general solution: sin x sec? x cos? y dx + dy = 0 a. sec x + tan y = c b. 2 tan x ++…

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Q: Let y(x) be the solution for the DE. y+y tan(x) + sin(x) = 0 If y(0) = In 2, then at x = %3D %3D the…

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Q: Two masses hanging side by side from springs have positions s1 = 2 sin t and s2 = sin 2t,…

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Q: Q: Classify and Solve dy sin x dx sin x sin 2x +y cos x

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Q: 2 Consider solving dx using a suitable trigonometric substitution. After performing substitution…

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Q: Find the solution. (y - cos?x)dx + cos x dy = 0 A) y (sin x +cos x) = c + x - tan x x (cos x + cot…

A: Solution

Q: 13. Find the general solution dy = sin x + y cot x: dx а. у %3D (х + с)(sec x + tan x) b. у %3 (x +…

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Q: Given: x = 0– sin 0; y = 1– cos 0 d'y Find: dz2 d'y dr? (1-cos 0) CO d²y dr (1-cos e) (1- -cos 0)…

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Q: 2. Find the length of the asteroid x = cos't and y=sin't , 0<t<2n. x = cos' t y = sin³ t

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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: 7. Find the general solution: ydx + (1+ x²) arctan x dy = 0 tan y = c b. arctan x + sin y = c C. y…

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Q: V 3 (d) r(1/6 + At) - r(n/6) = 3 COS At sin At cos At + SV3 sin At it

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Q: 2) sec?x tan y dy + sec?y tan x dx 0 Ans: cos 2x+ cos 2y = c

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Q: Which of the following equations is NOT an exact equation? (2x sin y + y)dx + (x² cos y + x)dy = 0…

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Q: For the equation y" + w?y = 0, Show that y(x) = A sin wx + B cos wx is a solution for all values of…

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Q: 2. Prove the following equation is exact and hence find its general solution. (y?sinx + xy?cosx)dx +…

A: Given: (y2sinx + xy2cosx)dx + (2xysinx)dy = 0 To prove that the above equation is exact. We also…

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: L 1) For f sin sin 2 2πmx 2nnx sin sin L dx , write the solutions for the following two sets m = 4,…

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Q: 8. Find a particular solution y,(x) to the equation y" +y – 2y = 5 sin r - in the form yp(x) = c1…

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Q: (1) Evaluate ædx Hint: Express cos* z in terms of sin z. Then use the substitution u = sin z. Back…

A: We can make it easier for you.

Q: dy when (cos x) = (sin y)* dx A Find %3D

A: Note: - Since you have asked multiple question, we will solve the first question for you. If you…

Q: d²y dy + 2y sin? x = e-cos * sin² x dx Solve : + (3 sin x – cot x) dx?

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Q: H.W: Estimate the root of the equation for the following equation using Secant Method: 1. x3-5x = 3…

A: We can have this using secant method

Q: 3 1 1 1 dx in terms of k. 6. If dy k, find 1+y 1+9x2 0 Sin (p tos - l tan + C

A: Given:

Q: A violin string produces a vibration u(x,t)=a sin(2t-x/ 137). cos(A-t)+b sin(14t-x / 137). cos(E-t)…

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Q: Solve for C using the form f(x,y)=C. Given [2x + ycos(xy)] dx + x cos(xy)dy = 0; f(1)-pi/6. decimal…

A: differential equation