d²x is dy2 15 If x = (3 2y)5/2 , then 15 А. — A. -15(3 - 2y)1/2 В. 2 (3 2y)1/2 C. - (3 2y)1/2 D. 15(3 — 2y)1/2 С. - 2

Q: Find d2y/dx2 implicitly in terms of x and y.

A: Implicit differentiation involves the treatment of one of the variables as a function of another and…

Q: 2. y"-y-6y = u(t – 1) – u(t – 4); y(0) = 1, y(0) = -1

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Q: D'y- 4. (4D - 4D³ - 23D2 + 12D +36)y = 0 5. (D° + 3D² + 3D + 2)y = 0 Dy +y = 0

A: The given differential equation is: (4D4-4D3-23D2+12D+36)y=0 The auxiliary equation is:…

Q: dy If 2y = xlnx, then dx (In x)xinx (xinx) In x (b) (d)(In x)xanx) 2

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Q: 2t -4 0st<2 D2-1)y= t22 y(0)=0, y'(O)=1 Find L{y}

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Q: S- dy - = 2/y- 5in|Vy+ 5| +C Vy +5 А) True B) False

A: ∫dyy+5Let y+5 =xdifferentiating on both sides12ydy=dx=∫2y dxx=2∫x-5xdx=2∫(1-5x) dx

Q: If x = 2t² + 3 and y = t* d-y – v2 then is 2 dx 1 a) 4 b) c) 2t d) None of These -

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Q: 1.n f csc n? de y2 - 2y + 3 2.5; Vy - 3y: + 9y – 21 dy

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Q: "-y'-12y=x * O y= C1(e^4t) + C2(e^3t) + (t)/12 + 1/144 O y= C1(e^4x) + C2(e^-3x) + (-x)/12 + 1/144…

A:

Q: d²y 54. Let y = 4r+2r+l_find CL)

A: To find the double derivative of below expression.

Q: (x.yız) (x,9e)x4か t. 22 P( 3-1,0) けこくりん)2

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Q: 5. (D³2D+4)y=0; y = -2, Dy = 8, D²y = 0, when x = 0.

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Q: 1. (D³ + 3D² - 4D - 12)y = 0 2. - d'x 19+ 30 = 0 dt3 dt 3. (4D4 - 8D³ - 7D² + 11D + 6)y = 0

A: 1). From the given differential equation; D3+3D2-4D-12y=0 So, The auxiliary equation is:…

Q: 3 '9-x2 3+V9-a2-y? 1 dz dy x² + y² x²+y² a C = L7I Fle,0,6) dp dộ do

A:

Q: y"(t) – 4y'(t) + 4y(t) = 4e2t; y(0) = 1, y'(0) = -4

A: Given differential equation y''t−4y't+4yt=4e2t and y0=1, y'0=−4. Take Laplace transform both sides…

Q: (D³– 4D°D'+ 5DD2 – 2D ) z = e'*2* + Vy + +2x +Vy +x. |

A:

Q: الرابع: جد ناتج احد التكاملين التالي ين 1- Smte) xy e*y° dxdy 2- r? N4-y² ry8-x²-y" zdzdxdy x²+y2 2-…

A: 1 ∫01∫0ln(2)xyexy2dxdy first we will solve ∫0ln(2)xyexy2dx ∫0ln(2)xyexy2dx=y∫0ln(2)xexy2dxSubstitute…

Q: Q.2 JJR ex2-2 dxdy, where R between x2 =-y, y = 0 and x = -3 , y = -9

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Q: 33. Y"(t) - 8Y(t) + 2Y(t) = 4t + 12e-t, Y(0) = 6, Y'(0) = -1. %3D Ans. Y(t) = 3ef-2et+ 2t + 3+2e-

A:

Q: -6 Let y = ( 5x + . Then dy - A(5x + )" (5 -)". = A 5x + where %3D B = C = D =

A: To find the derivative of y with respect to x

Q: Suppose that dæ dy 4y? and that y(1) = 3. Find y(x).

A: The explanation of answer as follows

Q: 4yy" + 2y' = 0 = y' =? A) y'= -In B) y' = In c) y' = 2n(cy) D) y' =-In E) = 4 1n

A: Given that 4yy"+2y'=0

Q: Find the Particular solution of the ODE d?y dy -6--7y = -9e-2x, dx2 at y(0) = -2 and y(0) = -13 %3D…

A: We have to find the particular solution of the ODE                       d2ydx2-6dydx-7y=-9e-2x at…

Q: x2/3 If y = ¤l/3 + 2 dy then le=-8 %3D da

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Q: dz (D2 + 16) (D² + 4D – 5) (D² + 2D - 3)*z = 0, Dz = dr

A:

Q: d²y 15. If y3 — ху %3D 5, then dx² 2ху - 2ху А. (Зу2-х)3 В. (Зу2-х)3 5 2ху С. (3y²-x)² D. (Зу2-2х)3…

A: Given, y3-xy =5  We have to find d2ydx2

Q: af If 2xy(-x² + y) + xe", what is ду ду? Select one: а. 4ху — 2x3 + хеУ ду? 2x(-x² + 1) + xe" b. ду?…

A: Given ∂f∂y=2xy−x2+y+xey

Q: 3x2-3-4e2x and y(0) 8, then y= If dx x3- 3x - 4e2x x3- 3x - 2e2x + 8 x3- 3x - 2e2x x3- 3x - 2e2x +…

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Q: dz If x4 – y4 + z - 3z = 2, then %3D %D dx a) 4x3-4y3 3-4z3 b) 4x3 3-4z3 c) None of these d) 4x3+4z3…

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Q: d²y 15. If y3 - xy = 5 , then dx2 -2xy В. (3y2-x)3 2xy А. (3y2-x)3 2xy С. (3y2-x)2 D. (3y²-2x)3

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Q: (D3 - 3D - 2)y =0; when x =0, y=0, y' = 9, y" = 0. 2x y = (-2 + 3r)e¯*+2e² B В y = (-1+ 2x)e2* + 2e…

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Q: f(x,y) = eY Then: 12zy fxxyz2= x2 2zy 13 12z y2 fxxy 1223y2

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Q: If x2 z2 + y² + xz3 = 3, then dz at the point (1, 1, 1) is: O b. Ос. - 3 d. - 3 Ое. f.

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Q: 3. D'y - D'y- Dy + y = 0 (AD4

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Q: dy Find dz given that y = -2 – 8z². z=-3

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Q: 5. (D2 – 5D + 6)y = 18x2 + 12e2* (Assume yp = Ax² + Bx + C + Ee2x)

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Q: (D² – 3D – 4)y = 0 is ° y = C,e** + C,e* " y = C,e** + C,e* 4х 4x -X -4x ° y = C,e** + C,e* y = C,e*…

A:

Q: a.) = y° (4 – y²) - b.) y' = y In(y+ 2) %3D c.) = (ye" – 9y)/e" -

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Q: (D³ – D)y = 4e * + 3e2x X. a. Ур а. у, — 2хе * + 2xe+ +-e e2x b. Yp = 2xe +e2* X- 3 2x C. Yp = 3xe 2…

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Q: dy If dt = -10e-t/2 and y(0) = 20, what is the value of y(6)? %3D 20e 6 20e 3 20e -2 10e -3 Se3

A: We are given the differential equation dydt=-10e-t/2 and y(0)=20. First, we will be solving the…

Q: dy If x2 + 2xy= y², then is x+y (A y- x B 2x+2y X +1 C y X-y D) 2(x + 1)

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Q: dy If ay = -x+4x -3 and y= 2 when x = 0 then y is equal to dx A y =-1+8x y=--2 B ²+2x- 3x +2 4 y =…

A: Solve the above questions.

Q: y(2x- xy ty')da-x (2x-y) dy =0, when x(4):0 %3D

A: Given: y(2x² - xy + y²)dx - x²(2x - y)dy = 0, when x(1/2) = 0

Q: 2) (r'y-2y kdx+ (y`x- 2x* \dy = 0

A: 2) Given that, x3y-2y4dx+y3x-2x4dy=0y3x-2x4dy=-x3y-2y4dxdydx=2y4-x3yy3x-2x4           ...(1)

Q: 7. (D+ 3)'y = 15x'e-3* 8. (D- 4)'y 15x²e**. 9. D (D – 2)²y = 16e2 10. D2(D + 3)²y = 9e-3x 11. (D² –…

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Q: 3 1 (x + 2y)dydx -1 a) 5 b)7 O d)-:

A: Please check step 2 for solution.

Q: dy if y = In dæ 3x + 2 \ 1/4 22. Find x2 – 5

A:

Q: 5. If x-2ry+ 3y² = 8, then dx %3D 8+ 2y -2x (A) 6y-2x Зу - х (В) y-x (C) 113

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Q: b. xy--2×y- ヴり C. 2x- xy - zy +> - xyy'+ 2xy'; when x 1 when X = 0, y-1 19=1

A: