The general solution of y" (x) – 4y'(x) + 8y(x) = cos(r) + sin(x) is %3D Select one: O a. e2 (c, sin(2r)+ c2 cos(2æ)) + cos(x)+ sin(x) O b. e2 (c1 sin(2r) + c2 cos(2æ)) + sin(z) + cos(x) O c. None of the other options. O d. e2" (c1 sin(2x) + c2 cos(2r)) + sin(z) – cos(x)

Q: Integrate S(cos x)e*+sin xdx B. et-sinx + C A. -e4+sin x + C c. e4+sinx + C D. e-4+sinx +C A В C D

A: Given: I=∫cosxe4+sinxdx  ....(1)   We know that; ∫eax+bdx=1aeax+b+C

Q: Four equations are provided below. Which equation follows from the Power Rule? I. (P)' = pr P 1…

A: Answer is option (a)  Because only equation 3rd follows the power rule .

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A: The given equation is; (ex + 2xy2) dx + (2cos2y + 2x2y)

Q: The general solution of y" + y = e + 5e2* is y = ei (A cos (*) + B sin )) + Ce-" + 응e2x 2 () V5z y =…

A: Given that  y"'+y=e^(-x)+5e^(2x) To find the general solution

Q: 1. If x'y" + xy' + (x². 4 - -y=0 Y=x sinx , and y= y,v. Which of the following x>0 equations…

A: Solution:    Given:                  x2 y"+ xy' +(x2 14) y =0, x.o                 y1 = x-12…

Q: Differentiate the following: a) y=-x²+x-5 (b) y = 10 + 2 3 (c) y = 2√x - X

A: According to Bartleby guidelines we are supposed to do the first three sub parts of multiple sub…

Q: (a) fr = 4xz2, fy = yz and f; = xz 2 sin (x), fy = cos(x)y and f: = e" z z + y? If, f = = frâ + fyŷ…

A: a) Given f=fx+fy+fz and F→=fx x^+fy y^+fz z^ and  fx=4xz2, fy=yz, fz=xz So, we have f=fx+fy+fz…

Q: If f(x) = cos(3r), then f(77)(x) %3D (A) 37 cos(3æ) (B) 377 sin(3x) (C) –37 cos(3æ) (D) -377 sin(3x)

A:

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A: Given: fx=3xcos-12x+4-19-3x2. To Find: f'x.

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…

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A:

Q: (D² - 9)y = 0. (A) y = e*(c,cos2r +c sin2x) B y = c,cosh 3x + c,sinh 3x y = c,cosh – 3x + c,sinh 3x…

A: Solution

Q: What is the general solution of the given equation, cos(x + y) + 2x + (cos(x + y) + 4y)y' = 0 OA.…

A:

Q: Consider the D.E. y+4y" 1- cos(2r). Then a suitable form of the particular solution can be written…

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Q: (D³ + 3D + 4D³ + 12D²) y = 32 cos (2x) +3e3 – 16 sin (2) -

A:

Q: f(x) = 2) f(x) = 1+2 cos 2x, 3) f(x) = 1-2 cos x %3D 2

A: (1)   Let the function be,   f(x)=x-1x   Find the domain of the functionf(x)=x-1x Here, the function…

Q: The general solution of (D3+4D)y 0 is y= e"(c,cos2x+c,sin2x) y=C+c2x+C3e ax B © y=c+c,cos2x+c3sin2x…

A:

Q: Find y = 223 [tan(3r+1)] 2° + ry – y5 = 8x2 = (x + 3)² (x² – 2x) -

A: The Product Rule : The Product Rule says that the derivative of a product of two functions is the…

Q: Solve the following equation for y(x): y" + 4y = 6 cos 3x + 20 sin 3x

A:

Q: d (c) (cos(2²) + In(3 – 2æ)) dx

A:

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 where y(x) is defined by d²y dr? (a) 3x2 – e2, (b) sin 3x + cos r, (c) 1+x – x2 + In r. - -

A:

Q: J sin(x)cos(2x)sin(3x) dx sin(3x)cos(3x) , sin(2x)cos(2x) , sin(2x) + + C 12 8 8 4 sin(6x)_ sin(2x)…

A:

Q: dy sin(r-y). dr Q(3) Find the general solution of %3D

A: we have to solve the given differential equation

Q: // (cos (a? + y³)dA where D: {(x, y) | 4 < x² + y² < 49} Find

A:

Q: If f(x, y)= cos(x +y), then- (+: O a. - sin (x + y) O b. - cos(x+ y) COS O c. cos(x+ y) O d. sin (x…

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Q: find dy/dx of the following:

A: Please refer to the image below

Q: y = 2z3 [tan(3z+1)] a + xy – y5 = 8x? y = (x + 3)² (x² – 2)

A: You didn't mention what should I do with the given equations and this problem is posted as calculus.…

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A: Topic:- application of integration

Q: (ii) Evaluate J dx. COS TI

A:

Q: What is the solution of 2 tan (cos x) = tan (2 cscx). (а) 0 (b) 4 (c) 2 (d) 6.

A:

Q: (xy cos.xy +sin xy)dx +(x² cos.xy +e' )dy=0.

A: We have to solve given problem:

Q: (b) Verify that f(x) = 2 cos(x) sin(1x). f(x) = sin(6x) + sin(7x) = 2 sin = 2 sin 6x + N 2 X COS 6x…

A: Given

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A:

Q: Find the solution. dy sin x x +2y = y(2) = 1 dx , X A y = (4 + sin 2 + cosx²)/x² (B) cy= (3 cos 2x -…

A:

Q: cos(2y) – 3x?y²]dx + [cos(2y) – 2x sin(2y) – 2x³y]dy = 0 when x = 0; y = 0 %3D

A: Let's find.