6y²dx- x(2x³ +y)dy = 0 a. x³yi = y#+ c b. x-3yi 2y+ c C. x³yi= yi+ c -y= 2y+ c d. x

Q: d²y 5. If y = 4sinx + x²cosx + 4x then find dx2

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Q: dy If y = (x +4)(x-9), then dx Select one: a. dy = 8x14 – 20x3 dx %3D b. dy = 8x7 - 20x° dx %3D C. =…

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Q: Dy/dy=x^2-y^2/2xy.     Y(1)=0

A: Given that: dydx=x2-y22xy and y(1)=0

Q: 4-у2 r2x+y dzdædy -V4-y2 Jo

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Q: 7. x+y (2r +2y-x)' at (0, %) -4 at (-3y3. 1) 8.

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: xy² + a-2y+ 3) dæ + a ydy – 2 (x+y) dy = 0, when a = 1; y = 1 %3D

A: Given differential equation is  (xy2+x-2y+3)dx+x2ydy-2(x+y)dy=0

Q: d'y 2y If x + y = xy, show that dx2

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Q: 73. sc1X-7)-3 dx y= 11x -7 dy= 11dx = |1x-7 # dy %3D Sy3 tdy <-3 -3 y° dy -2 + C %3D + C It (-) + C…

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Q: ux.ュメトXス1いスコ-Y Palx, utェッズ)-。 入2コメ; +メュ-」+5- メレ 2 d、しズuメッ]= xit Xzメ]-6 fnd in Ganeral rm.

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Q: Non Homogeneous: (D2 − 7D + 6)y = 3x2 − 2x + 5

A: Here we have to solve the non-homogeneous differential equations     (D2-7D+6)y = 3x2 - 2x +5 .

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

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Q: Resuelva yDx - 2(x+y) Dy=0 O x² + 2y = cy² Ox+2=cy² O x + 2y = cy² Ox+2y=c

A: Given differential equation y D x-2(x+y) D y=0 The objective is to solve the differential equation.

Q: Find dy for the given values of x and ∆x. ; y = 2x3 + x2 - 4x; x = 2, ∆x = -0.2

A: Find dy for the given values of x and ∆x.

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

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Q: Find y, of+ 3+2y 14x2 + 42x + 6 d'y dx a.) y, = 7x2-4 b.) y, = 7x2 + x-5 c.) yp 7x2-x- 3 d.) y, =…

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Q: d3y find 3 5) If y = 4x + z %3D dx3

A: Given that: y=4x3+3x2

Q: y = C + Cze-$t O y" + 5y = 0 O y" + y = 0 O y" - 5y = 0 O y" - y = 0

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Q: y(t) = y" - 3y' = 8e²t - 2e-t, y(0) = 1, y'(0) = -1

A: Given

Q: y(t)+5 y(t)+4y(t) = 2e" -21 %3D

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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: dz Find at (2, -2, 1) if x² + y? + z2 6xz + 6yz + 21

A: Given equation is x2+y2+z2=6xz+6yz+21 We have to find ∂z∂y at 2,-2,1

Q: q. r. √y² - 25 -dy, y > 5 y³ dx x²√√x²-1 2 ,x > 1

A: Solve both integral as following:-

Q: d. x+3y = 0 y-4+ 4(x - 2) f. -6x + 4y -7 Find intercent and v-intercent.

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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: 10 Let y = ( 2x + Then -A(2x + 10)" (2- 10)°, dy = A[ 2x + 2 - where A = %3D C = %3D

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Q: d²y B Show whether y = Ax² + · x2 is a solution for x2- dy + x dx + 3y = 0 or not. dx2

A: If y=Ax2+Bx2 is a solution for x2d2ydx2+xdydx+3y=0...(1) then it satisfies equation (1).

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

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

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Q: + y²) dæ – x (a² – y²) dy = 0 r (x2 - y? dr + (x2 + 3ry + 4y) dy = 0

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Q: 4. (D3 – 4D² + 4D)y = 0 5. (2D4 – 3D3 – 2D²)y = 0 - -

A: (4). The given differential equation is: D3-4D2+4Dy=0 So, the auxiliary equation is: m3-4m2+4m=0

Q: Q5: 6y²dx-x(2x² + y)dy == 0 (Linear BernoullLeq.)

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Q: dy 3y y torh(x) + 2

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

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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: 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: dy 16x 3 If x° + 3 + y° = 8 then show that dx? %3D y5

A: Given: x3 +y3 = 8 To show: d2ydx2 = -16xy5

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: 2y³ + y_dy y* + y2 + 1/ 6y /9 + e-6y -

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Q: f(x,y) = 3y3 – 2xy + 12y – 3x² – 8x – 16 then fy equals ух

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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

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Q: 23D + 12D + 36) 5. (D + 3D² + 3D + 2)y = 0 6. (D3-4D2 + 7D)y = 0 7. (D + D)y = 0 %3D

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Q: dx Vx²-4x-7 7. dy y2-8y+5

A: