= -21e 2 C D +4 D +9D t1o)y 4. /f x-O -4 l 10

Q: (D² +D- 1)² y = 0 , when x = y = 0 , y' = y" = 1, y" = -1 %3D

A:

Q: d = V(22 – a1)° + (42 – Y1)² %3D - - (8, -3) and (-5, 6)

A:

Q: y" – 7y' + 12y = 3t?e4t – te3t sin t -

A: Given:  y''-7y' +12y =3t2e4t -te3tsint

Q: S-メー1)J r8-2) Cx+3) Cx+V)

A: Given,        ∫x2-x-1x-2x+3x+4dx

Q: 4. (D² +D-1)² y =0 ,when x= y = 0, y' = y" =1, y" = -1

A:

Q: 10. (D² + 4D + 5)y = 10; when x = 0, y = 0,y' = 0 %3D II

A:

Q: dy x²(y²+3) + = 0 dx y(x3+1) (final answers should be in terms of C)

A:

Q: - y² + 22 = 169 at (5,0,12). %3D (1) . i+3 3 3 -) i+ k, 6. 12 12 =) i+k, (d) k. i+

A: In this question, the normal to the curve is calculated using the finding gradient of the function.…

Q: Q₁ /Find x, y E R for: -i+1 2-i c) √

A: To find x, and y for the below complex number. −i+12−i

Q: I. (a + y?) da dy dz; 2: 2<4-a? - ở, z 20 (x².

A:

Q: (D³ + 4D² + 9D + 10)y - 24 e*; when x = 0, y = 0, y' = -4, y" = 10. %3D

A:

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

A:

Q: d²y if x = t- t? and y = t – t³. dx² Q 1. Find

A:

Q: If x = r +t, y =t° - 5² +9, then at t=2 is dx D a. 8. O b. -8 5 D C. - 5 8 d.

A: Find differentiation of x and y with respect to t and then divide to get the final result.

Q: d (3y? + 4y +2 Find dy y

A:

Q: Find ƒx (x, y)  and ƒy( x, y) .

A: fx(x,y) is the rate of change in f(x,y) in x-direction. We can find the same by finding the…

Q: Let f(x, y) = 160 2x2-3y² 2a? – For which value(s) of y is f(4, y) = 10? y =

A:

Q: السؤال الأول: جد باستخدام التحويل x = V5rcos(0( (0)2rsin , y = ناتج التكامل * dxdy е 5

A: We have to use proper integration substitution.

Q: f(x, y) = 3x – 2y x² + 2 + 2y? = 275

A:

Q: dy - = 2/y- 5in|Vy+ 5| + c Vỹ+5 A) True B) False

A: As per our guidelines we are supposed to answer only one question i.e. the first problem. For the…

Q: dy Given that x = 213and y = t? + 5t, then dx OA t+5 O B. 2t + 5 21? OC. 2t + 5 OD. 6t 2t + 5 O E.…

A:

Q: EX. (D* – 5D³ + 6D² + 4D – 8)y = 0

A:

Q: e where r is jiven peu'ametor! Fnd f'6).

A:

Q: x = u3 + 7 ; y= 6u? – 1 d²y ---> dx2

A:

Q: dy Evaluate from the equation vx + y = 1 + x*y² when x = 1 xp

A: Given equation √(X+y) =1+x2y2 We can use the following  identities   to solve the equation…

Q: (b) т Vi + 1, y = t3 – 12t for t > 0 Fイ

A: According to question given that x=t+1, y=t3-12t for t&gt;0

Q: ,-(ax²+2bxy+cy²) dædy = e (Hint: Let s = x+By and t = yx+8y, where (ad – BY)² = ac-b². Then ax?…

A:

Q: * dy -a 2. 2xydx 2) yy +36 X =

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

Q: f (x, y) = v/2x² + y?

A: I Have provided this answer in step-2.

Q: Ve da 6. Given x=- 1 a = 3x +2x-1 and and y=- find 2 de c-4

A:

Q: dy 2. a-y = ry, y(2) = 0 dr

A:

Q: dy Given that x = 4:3and y = t + 2t, then dx O A. No correct answer OB. 2t +2 12t? OC.t+2 4? OD. 2t…

A:

Q: dy r +3x+3 Find if y= I + 2 da dy da

A: Given query is to find the derivative of the expression.

Q: 2 V4-x2 e*²+y* dydx =? -2 0

A:

Q: F(s)= 2s+8s+12 f(t)=?

A: according to the question we need to find the inverse Laplace

Q: dy un 3 sec2 5x, w dr

A:

Q: x*y" - xy' + y = x Answer y(x) = c1 + c2x In x +t 16

A:

Q: 11. (D³ + D)y = sec? x when x =- 4 = %3B

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

Q: as Find w = 1° + 2y? I = r - s; y=r+2s2

A: Given:w=x3+2y2x=r-sy=r+2s

Q: dy 9. If x? + y² = 16x, then dx 8+ x y 8 y 8 + x C y 8 - x D y

A:

Q: D³ + D² + 4D + 4)y = 0; y(0) = 2; y'(0) = -4; y"(0) = 2. Find y(TT) %3D

A: Given that:D3+D2+4D+4y=0   y0=2 ,y' 0=-4,y''0=2To find: yπSolution :D3+D2+4D+4y=0Auxiliary…

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

A:

Q: dy Given y = 2u? and u = 8x – 1, then dx - 8(64x? – 2x + 1) 0 خيار 4 48(8x – 1)2 0 خيار 3

A: The derivative of xn is calculated using the formula, ddx(xn)=nxn-1 .

Q: = -4rt ; when t = 0, r = ro 1. 2. xyy' = 1+ y? ; when x = 2, y = 3

A:

Q: メP d4-ex+5y, Where y=0 when x=O

A:

Q: 4. (D² +D-1)²y = 0 ,when x= y = 0 , y' = y" = 1, y" = -1

A:

Q: f(x, y) = /4x? + 2y² f-( – 3, 1) = |

A:

Q: Solve the system:

A: Given: x+y=1                                                     ..1x2+y2=25…

Q: f (x, y) = 3x² + y³ + 4xy² + 8 What is the value of df (x, y) dy when x = 2 and y = 5?

A:

Q: y? dy 4-7 2.

A: