t3 - 1-2vt f(t) 3D -t5

Q: Vy - y 3 b) dy 2 y²

A:

Q: 2.x' + y' + x + y = t² + 4t x' + y' + 2x + 2y = 2t² – 2t

A: Given system is first order non homogeneous system of differential equations. Each x(t) and y(t) has…

Q: 2x+y 4ー dそdXdy -V4-y2

A: Triple integral is an integral of an integral with respect to three different variables. the…

Q: (D3 + 4D² + 9D + 10)y = -24e* %3D

A: Let's find.

Q: 2) (D² + 2D + 1) y = [exp(x) - 1]-2 %3D

A:

Q: f(x, y) = 75 + 8x+5 Find fx, fxy, and fxyx. 8x³ e-8y

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Q: f'(x) = z - 4r+ 12z + 12 and f(0) = 7.

A: f'x=x15-4x3+12x+12  &  f0=7 Integrating on both sides with respect to x, we get ∫f'x…

Q: 1. (D³ - 3D²D + 3)y = 0

A: To Solve: (D3-3D2-D+3)y=0.

Q: dx 19. Evaluate using substitution f V5-4x-2x2

A: I have used method of substitutions

Q: fy = √2 – 3x², find d'y dr2

A: Given query is to find the Indicated derivative.

Q: 3 11. f(x) = Vx-6Vx 12. f(t) = t3 -t3 +4 ww-

A: Basic derivative formula can be used to solve the questions. ddx(xn)=nxn-1ddx(cosx)=-sinx

Q: Sx, y) = 2r - 3y²

A:

Q: Find d²y/dx² for the following equatio: f) x2/3 + y2/3 = 1 g) x³ + y4 = 16

A:

Q: 3t y" - y' - 6y = t²e³t - 4t², y(0) = 0, y' (0) = -1

A:

Q: c. The f'(3) for y = v3x² + 9

A: c)y=3x2+9

Q: f(x, y) = 2y – 6ry - x 2.

A:

Q: æ = 4;y = t-1»Y t² – 1|

A: Use the following derivative formulas:ddxxn=nxn-1ddxfxgx=ddxfxgx-ddxgxfxgx2ddx ( f(g(x) ) = f'…

Q: (D³ -3D* +4D³ -8D² +16),y = 0

A:

Q: y = (t² – 2)². a²y = t2 dx²

A: Derivative Question

Q: 8. (D2- 2D+ 1)y = xlnx

A:

Q: (r2+2rt-4t2)dr-(r2-8rt-4t2)dt=0

A:

Q: (D³ - 3D2 + 9D + 13)y = 0

A:

Q: F(x)= V3 j 9(x)= 9x-8

A: Given  functions f(x)=3       and   g(x)=9x-8 we need to determine  (f+g)(x)

Q: [D³ – D)y = -2(1+x) + 4e* - 6e¬* + 96e3× %3D

A:

Q: d²y x-9 Find for y dx2 = (3x² –2x+5)

A:

Q: 2t + 7 f(t) = t- 3 %3D h(n) = - 2n2-3n+1 %3D f(h(-1)) =

A: Here we have two functions f(t) and h(n), we want to find the value of f(h(—1)). To find f(h(—1)),…

Q: y" - 2y' + y = 4e-t + 2et, where y(0) = -1, y'(0) = 2

A:

Q: (D³ – 3D + 2)y = -7 у" - 9y' %3D 27

A: (1).    The given differential equation is: D3-3D+2y=-7

Q: f(x) =D V4- x2 1는 Jf %3D (-2,2) .1 (-00, –2) U (2, 0) 2 (-0, 2] U [2, c0) 3 [-2,2] .4

A:

Q: y = (t² – 2)². a²y 2. dx²

A: y=t2-22 and x=t2 Now, differentiate the given function with respect to t.…

Q: Sketch the fol 2 -4y a-. b- y2 -4y 3(y - 5)2 C-

A: As per guidelines, we will solve first three subparts: a. Given equation is  y2-4y+8-4x2=0 Rewriting…

Q: * (D-2y'y(x) -0 d Ja -1

A:

Q: (D³ - 3D² - 6D + 8)y = xe

A:

Q: f(x) = (4e2x)3 3(4e2*)2(4e2x) 3D3(16e**)(4e2*) 192(e6x) %3D %3D %3D

A:

Q: Find d2y/dx2 simplify in terms of x and y x2+y2=4

A:

Q: Evaluate d2y/dx2 at the point (0, -9). x = t3 - 3t y = 3t2 - 9

A: Given: x = t3 - 3t y = 3t2 - 9

Q: f(t) = e*(t² – 2t + 2).

A:

Q: d4y Q4\ b) Find : Y=3X³-4X²+7X+10 dx4

A: Given: Y=3x3-4x2+7x+10

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

A:

Q: 3t X : || 1+t³ 3t 2 y 1+t3 t + -1

A:

Q: d) y = - + 3 e) y = 20.5x f) y = V2(x – 6)

A: Given query is to find the transformation performed and then graph the function.

Q: e3x (D³ – 3D² + 2D)y 1+ex

A: The given question can be solved as shown in step2.

Q: f(x,y) = x² - xy +y² – 9x + 6y + 10

A:

Q: 2s -5t f(s,t) = %3D 4s +t %3D f =

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: y" - y' - 6y=t²e³t — 4t², y(0) = 0, y' (0) = -1

A:

Q: (a) y = -T (b) y = 2x° + 3x (c) y = x² + 5x 7 (d) y = x(x - 1) %3D -

A:

Q: (x = s² – t² y = s·t³ z = 2x – 5y,

A: See the attachment

Q: d²y Find dx2 x = t* - 8, y =t – t2 %3D

A:

Q: t²y" + 3ty' + y = 0, t> 0; y₁(t) = t-¹

A: t2y''+3ty'+y=0, t>0; y1(t)=t-1 lets use method of reduction of order to find the second solution.…