Solve 16dy 4-y)dx Oa. 16sin x+c + C O b. sin (y) = 16 on O c Bsin -x O c: 8sin d. 16sin (y)= x +c

Q: Find the solution of y" + 9y' = 162 sin(9t) + 1296 cos(9t) %3D with y(0) = 5 and y' (0) = 9. %3D y =

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Q: (p² –1)cos[cosh (In r)]dr

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Q: Show that 0, if m if m + n sin(nx) sin(mx) dx T, = n IT

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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: 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: Find Y'and y" Y = sin (x²) Y = 2x² cos (x²) 2 y" = ? 2

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Q: Use undetermined coefficients method to solve b. y" – 2y' + 5y = e* cos 2x %3D

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Q: T/2 1 Vi- sin z dz = 2

A: Evaluate the integral 12∫0π21-sin2x dx

Q: Find a particular solution to y" + 36y = 24 sin(6t). %3D

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Q: y" + 2y' = 2 – 5 cos(x), y(0) = 0, y' (0) = 1. %3D

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Q: What is the complete solution of -2+y = +y=x-2-2 cosx. a.) y. = Ae*+ Bxe* + sin x - cos x b.) y, =…

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Q: 8- Evaluate a) Sz? + 4 sin(8z) dz 1+9cos(8z) бх- х2 b) S 3x. csc² dx x3-9x2+8

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Q: Find Duf at P. 3 f (x, y) = sin(3x – 4y); P(4,3); u = j - - NOTE: Enter the exact answer. Duf = |

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Q: where yco,t) = y (5,t) = = 2Jx2 and y cx, o) y (X,o) = 10 sin 4T X

A: We solve the differential equation by the method of saperation of variable. In this method we…

Q: 2z2 cos 5z dz EVALUATE.

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Q: y""+y" = 3x² + sin x − 2 cos x -

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Q: Find the GENERAL SOLUTION. 1) ex-ydx + sin y sec x dy = 0 2) y(u? + 1)du + (u³ – 3u)dy = 0 %3D |

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Q: rcosA 2. r sin 0 dz dr de

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Q: Determine c1 and c2 so that y(x) = c1 sin 2x + c2 cos 2x + 1will satisfy the conditions y(?/8)= 0…

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Q: In y = C, sin 8x + C cosax + 9x²- 2

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Q: Calculate x²+y² =4 and Sin (yetp) dA,D between. ty2 = 16 abore y=0 2 %3D

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Q: Find a particular solution to y" +4y = - 12 sin(2t).

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Q: What is the general solution of (r +sin 0 cos 0) dr + r (sin 0 + cos 0) de = 0 ? - rsino rcose = C…

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Q: 2: Clasafy ad Solve The fllowing diffrential equatóns dy -2x e + + 4. Sinx フス2 フィ* + (6 y = 6x°1ox…

A: The general solution of an ordinary non homogeneous differential equation is the sum of…

Q: SV1- x2 sin-1x dx

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Q: Qq / show thot ifa is a constont then, u(X,t) = sin lat) cos (x) is a solution to

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Q: What is the particular solution of (Dª + 4D² – 1)y = 44sin3x O a. cos3x O b. cos2x O c. sin3x O d.…

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Q: ind the solution of with y(0) 2 and y/(0) = 5. = = y" + 4y = 96 sin(4t) + 96 cos(4t)

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Q: The equation (3xcos (3x) + sin(3x) – 3) dx + (2y + 5) dy = 0 is exact. Solve it. xsin (3x) + y + 5y…

A: according to our guidelines we can answer only three subparts, or first question and rest can be…

Q: che general solution of -V - 6y = 6x3 + 26 sin 2x

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Q: Find the general solution of y(4) + y" = 3t2 + 4 sin t – 2 cos t

A: Given differential equation is y(4) + y" = 3t2 + 4sin(t) - 2cos(t)

Q: Find a particular solution to y" + 16y = 16 sin(4t). Yp

A: The given differential equation is:y''+16y=16sin4t        ...............(1)The auxiliary equation…

Q: dz Find a? sin(2y – 5z) =1+y cos(6zx)

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Q: with y (0) = 7 and y' (0) = 2. y" + 9y' = 162 sin(9t) + 648 cos(9t) y =

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Q: -Solve b exact (Di sferential Egmation) Q 1- (3X+y Cosx) dx+(stux-uy)dy=o

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Q: With the substitution u = sin(x), we get | 11 sin2(x) cos(x) dx = 11 u2 du. u? du. 11 %3D which…

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Q: -41 sin tZ dz, c: 1Z-il=2 z4 ans: 3. coshz dz ,C: IZ1=1 27T ans :

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Q: Find Duf at P. 3 4 f (x, y) = sin(x – 5y); Р(5, 1); u = i и %3 - - NOTE: Enter the exact answer. Duf

A: This is a directional derivative problem

Q: Solve the DE by Method of Undetermined Coefficients y" +5y +4y = 90 sin 4r y (0) = 1, y (0) = 2, y"…

A: Given that y''''+5y''+4y=90sin4x Now take the homogenous term, y''''+5y''+4y=0 Take m=ddx,…

Q: 8. (sin°(5y)dy

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Q: z = 3e*jS, y = 3z2 + sin(z) iS l5 al: Jis dx

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Q: Find the general solution Solution 8. y= c, +c, cos 2x+c, sin 2x- 7 e* cos 2x+ 85 6. e* sin 2x 85 8.…

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Q: 9. y = 3 sin įx 11. y = 4 sin mx 10. y = 2 sin x 12. y = 3 sin 2mx

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Q: Solve the ivp y′=sin^2(x−y)    y(π/2)=π4 Solution is y(x)=

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Q: .2π π 1 -εrocos? θ r dr sinθdθ φdφ x 32 πο X = ?

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Q: For u = ex cos y,(a) verify that ∂2u/∂x∂y = ∂2u/∂y∂x;(b) verify that ∂2u/∂x2 + ∂2u/∂y2 = 0.

A: The given  function is, u=excosy (a) To verify ∂2u∂x∂y=∂2u∂y∂x Solution: We have u=excosy…

Q: What is the general solution of sin 0-2rcos²0) dr + rcos0 (2rsind + 1) de = 0 ? %3D O sin 0 rcos²0…

A: Given differential equation is: sinθ−2rcos2θdr+rcosθ2rsinθ+1dθ=0

Q: 2. Solve the IVP y(3) + y" = 5 cos(2.x), y(0) = 3, y'(7) = 1, y"(0) = 0

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Q: What is the general solution of (r + sin 0 cos 8) dr + r (sin 0 + cos 0) d0 = 0 ? %3D rsind rcose =…

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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.