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: fr cos xdx

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

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: 7- y" + 4y = cos x, y (0) = 0, y(n) = 0

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Q: x*y"+xy'+(x? y=x cos x 2. Show that is a solution of the equation

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

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Q: Consider the following IVP: у" + у'%3D -сos x; у(0) %3D а, у'(0) 3b Find the general solution. 1 1…

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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: Find all complementary functions of the equation y" - 4y' + 4y = 0. a. cos2x, sin2x b. e-2x,xe-2x C.…

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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: If x²y" + xy' + (x² – ÷)y=o x >0 ,V,=x 2 sinx , and y =y;v. Which of the following equations…

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

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Q: 3. Find the derivatives: a) f(x) = 3x³-4 2x²+3 b) DO NOT SIMPLIFY y = (x² + 6x + 2)(²+√x + 3) c)…

A: Given; a) f(x)=(3x3-4)/(2x2+3) b) y= (x2+6x+2)(2/x4 + 3sqrt(x5) +3) c) g(x)=-2csc7x+8sin3x+12tan2x…

Q: y" + 8y' + 25y 2t-e-4t + 5 cos 3t

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Q: Q1:-/ Verify by direct substitution that y, = epx cos qx and y2 = ePx sin qx , are solutions of the…

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Q: 1 = x²y" + xy' + cx? - +»v=o x>0 ,V1=X sinx , and y =y,v. Which of the following quations satisfied…

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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: • If y = cos x2 + x² then y(4) = 8x? sin x² + 0 TO F

A: Topic- Derivative

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

A: Compute the derivative as follows.

Q: ry"+xy'+(x* -y =0 -)y = y = x cosx is a solution of the equation Show that

A: Given               x2y''+xy'+(x2-14)y=0                      (1)

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: (1) y "'+ y "– 2y = 3+2cosx

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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 f. f "(x) = 5 + cos(x), f(0) = –1, f(9/2) = 0 f(x) : %D

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Q: xt' + (t")3 = Và +5 x (3y')² ex² - y² = = (4x²y³ + y)²¹ y" 4 (cos x)² - y"

A: The given  differenrtial equation is xt'+t''3=x+54 Calculate the order of given differential…

Q: Find the general solution of y'"''- 6y'"+2ly'– 26y=0 A y=c,e-+cze* cos 2x + c,e*sin 2r ® y=c,e+c,e…

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Q: y= (12,4 + x)* + (1+)(Va² +x- c )cos²(4x), c)cos²(Ax), 3)4( 3 y = (12,4 +x)* + (1+x' Зx +x — с y = ?

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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: In implicit differentation problems it seems we treat x and y differently. For example, when we…

A: Recall: Chain Rule of differentiation :    If F(x)=f(g(x)) then ,   F'(x) = df(g(x))dx =…

Q: 2/x?y" – 2xy' + 2y = x³ cos x

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Q: A particular solution of y" - 3y' – 4y = 2sinx 5 -cosx 17 a. 3 COSX - 17 5 sinx 17 b. 3 -sinx 17 C.…

A: find roots for the homogeneous system

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.