A particular solution of x²y" + xy' + (x? – 0.25)y = 3x3/2sinx, x>0, y,(x)=x-1/2sinx, y2(x)=x1/2 cosx -cosx 1/2cosx a. 34/3sinx b. 3 x coSX 4 C. - - x1/2cosx d. 3 e. -x1/2sinx - - X 4

Q: What is y' of y = sin¹ (cos x)? O A. y' = ATHE sin + 1-cos² 1 O B. y' = 1 OC. y'= sin z 1-cos² z OD.…

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Q: 1 - cos 2x if y = prove 1 + cos x y' = 2tanx.sec²x

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Q: Q3) Simplify (if necessary) then Compute: y"+ 2y Where y(x) = (zx+ cosx*)] [4(cosh2x-sinh2x)] d 2,2…

A: To find -  Simplify (if necessary) then Compute : y'' + 2y' where yx = ∂2∂x ∂zz2x + cosx44cosh2x -…

Q: Find the form for a particular solution to the equation y "+2y'– 3y =r?cos (nt). A…

A: I am going to solve the given problem by using some simple calculus to get the required result.

Q: Find one solution of y" + 2y' - 2y = 3e³* cos(2x).

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Q: 6. Find dy dx of cos y - 2xy + 3x = 2x sin x

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Q: Find the solution. (D3 +7D2 + 19D + 13)y =0; when x =0, y=0, y' =2, y"=-12 (A y = e*cosx B y =…

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Q: If x'y" + xy'+(x? -y=0 x>0 ,y,=x 2sinx , and y=y,v. Which of the following %3D equations satisfied…

A: Let   y1 and y2be two solutions of the second-order linear differential equation d2ydx2+Pxdydx+Qxy=R…

Q: If x'y" +xy' + (x2 - -0 x>0 , V1=X 2 sinx and y=y,v. Which of the following equations satisfied by v…

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Q: y" y'' +(cos xc)y' + ну =0

A: As per the question we are given the following second order homogeneous differential equation : y''…

Q: Find f. f"(x) = 5 + cos(x), f(0) = -1, f(9π/2) = 0

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Q: Which of these functions (or none of them): (1) z=e" (ycosx-xsiny) or (2) z=e' (y cosx-xsin x) 0²z…

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Q: Solve y' = cos(2x + y – 5) – 2. = COS

A: The solution is given as

Q: Is the equation separable, linear, bernoulli, or homogenous? dy а. dx x4 + 4xy² 2x3 + x²y +y³ b.…

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Q: If x³y" + xy' +(x? -y=D0 x>0 ,y,=x sinx , and y3V,v. Which of the following 3 equations satisfied by…

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Q: Find the solution. y'= 1 + 3ytanx (A) 3y tan³x=c+ 3sinx-cos³x B 3y cos³x=c+3sinx - sin ³x D 3y…

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Q: let y=[cos(2x-π)]3 Find y' at x=(π/6)

A: Compute the derivative as follows.

Q: Solve the equation y' + a = eax +)csc(ax+y), where a is a real number Select one: a. e-(x…

A: The differential equation is given as y'+a = e(ax+y)csc(ax+y)                          (1) Let ax+y…

Q: Find f. f"(8) = sin(0) + cos(8), F(0) = 5, f(0) = 4 F(8) -sin(0) – cos(0) + 5x + 6

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Q: Find the solution. y'= 1 + 3ytanx 3y cor x=ctanx + 3sinx – sin³x 3y tan?x=c+3sinx – cos?x © 3y…

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Q: Find y" if y = 5x sin x. O A. y" =5 cos x- 10x sin x O B. y"= - 5x sin x OC. y"= - 10 cos x+ 5x sin…

A: Solution: The objective is to find the double derivative of the given function

Q: COs ax dx. x² + b² (q)

A: Cauchy residue theorem: If f is holomorphic function defined on simply connected open set with…

Q: 2/x?y" – 2xy' + 2y = x³ cos x

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Q: The general solution of x*y = -x³y- csc(xy) is A 2x?сos(xy) - 1 %3D сх B 2x²cos(xy) +1= cx² c)…

A: We have given a differential equation ,  x4y' = - x3y - csc(xy) x4dydx = -x3y - csc(xy) Here , plug…

Q: 2.) y"-3y'+4y = sint ; y(0) = 0, y' (0) = 1 The answer should be: (1/6)cos t + (1/6)sin t -…

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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.