Find the general solution to x'y" + 3x y +5y=0 (A) y=x Acos +Bsin (B) y=x Aco Acos In +B sin In (C) y=x"[Acos(21n| x}) + Bsin(2 1n| x|)] (D) y= Ax+ Bx (E) y= Ar+ Bx

Q: 2x a) y" + 4y' + 4y x2 b) (D* + 8D2 - 9)y = x2 + sin 2x

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Q: 5) y"-y'-2y=x+cosx

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Q: What is the general solution of (1 + a2) y' = x*y %3D Oy"-3ay + 1 = C O ay - 3ry + 3y% tan-1 æ + 1 =…

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Q: find the general solution for  2 Z_xy+ Z_yy =cos( y) +1

A: Firstly find a homogenous solution and then find a particular integral . hence complete solution =…

Q: If y = 12y sin(4z) – 12z sin(4y), then (z, y) = 6y? sin(4z) + 3z cos(4y) + h(x) O (z, y) = 6y²…

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Q: cos(2) is equal 1 اخترأحد الخيارات 2-2 sin(z) dy dx dz 2 – z 4-2 r/2 sin(2z) dy dx dz 4 - z z-2 cx/2…

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Q: Let y = eex + sin(2x), then Y + y' is equal to 2x A 4e2x + 2 sin(2x) (B None of the given choices ©…

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Q: This is the solution of the Cauchy - Euler equation xy" + 5xy' + 20y = 0 %3D O y = C1x4 cos(4 ln(x))…

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Q: A particular solution of x²y" + xy' + (x? – 0.25)y = 3x3/2sinx, x>0, y,(x)=x-1/2sinx, y2(x)=x1/2…

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: ах ) x' + 4x/y 5 y² = 3 ) Vxy +1 = y ) 3xy = (x' + y' ) ) x' +x.tan¯' y = y ) sin¯'(xy) = cos"' (x –…

A: Simple differentiation

Q: Which of the following is a solution to x'=A(t) x + b (t) if a) v (t) = b) O v (t) = v (t) = d) ○ v…

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Q: D- y" + 2y' + 5y = 6e2* + x sin? x + e*cos 2x %3D

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Q: = )* - a) Va' + 1) zVx +1 +C b) Va' + 1) - 2V +1 + C Q3: S dx%3D c) V + 1

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: نقطتان )2( What is the Form of the General * ?Solution for this equation A. y(x) = Aem; + Bem;x dy?…

A: Given,  dy2dx2+dydx-6y=0

Q: 4) Find ôw/ ôr if w= (x+y+z)*, x=r-s, y = cos(r+s), z = sin(r + s) the point (r,s)= (1,-1)

A: Given - w = x + y + z2 , x = r - s, y = cosr + s, z = sinr + s To find - Find ∂w∂r at the point r, s…

Q: The general solution of y" + 4y' = 12 can %3D be written as (A) y = c1+ c2e¬2= + c3e2 + 3x (B) y=…

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Q: Q7: Í sin(3z)cos(4z) dz = a)cos z- cos(72) + C b) -tcus x -os(Ix) + C %3D Qe S sin'x cas d = 2).

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Q: 32) Find ур(0) for the equetion y (4) - y" - 2y + 2y = 3xe³ + cos x

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Q: | (6e"+6x° +4 cos x + 2)dx = %3D 6e + x° + 4 cos x + 2x + c O e – x° + cos x + 2 + c 6 O e + x° 4…

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Q: Can you explain how all A B C D terms are calculated

A: Solution of the given question is like as

Q: Let y, be a solution to y" + zy +r'y = cos (z) and y, be a solution to y" + zy' + z*y = sin°(z).…

A: Given that y1 be a solution of y''+xy'+x2y=cos2x and y2 be a solution of y''+xy'+x2y=sin2x. That is,…

Q: -7x f(x, y) = e" sin(4x + 5y) af e^(-7x)(4cos(4x+5y))-7sin(4x+5y) af 5e^(-7x)cos(4x+5y) dy ||

A: Partially differentiate with respect to x and y by using product rule.

Q: Solve: (2x cosy + 3x y) dæ + (x – a? sin y – y) dy = 0 O 2x cos y + 2x2y-y = C O x3 cos y + x?y-y =…

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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: Evaluate f(e' + cos(30) de 1 [ (x³ + cos(3.x)) dxr x sin (3x) ,. a) 4 r* sin (3x) b) 4 3 3 x* sin…

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Q: If z = x2 – y2 and x t cos 2r and y = r sin t, then %3D a2z is ar2 (A) 2 cos (2r) + 2r? cos?(t) –…

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Q: (D-9)y 3e" +x-sin 4x. 3 1 A. y C,e*+C,e* +e* +÷x- sin 4x 25 -3x 8 3 1 B. y Ce* +C,e-* +e* -x- sin 4x…

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Q: Z= x³+y¹+(x sin y)+ (y cos x),Zx/Zy= (3x²+ sin y-y sin x)/(4y+ xcos y -cos x) O True O False

A: Given Z=x3+y4+(x siny)+(y cosx)To find ZxZy:

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.