3t X : || 1+t³ 3t 2 y 1+t3 t + -1

Q: m (x) = V - 6x 1. f (x) VI +2-3 1 t(z) V9 - 1 9-r

A: we have to find the domain for the following function

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: ) xy' + 4y = x², with y(1) = 0 2) y'- -

A: We shall solve first question only per answering guidelines. For others please post again by…

Q: Find: ydy-xdx (x2+y2) 0< x<1 & 0 <y<1

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Q: If f(x,y)=xe"*/2+135x?y3, then əx²əy³ at (1,1) is equal to

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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: d?y 13 으18 + t6/3- t2 + 246 3 Find if y(t) - dt2 3

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Q: dy * + 2(t + 1)y² = 0, _y(0) = - ip 1/8

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

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Q: f(t)=t²(3-2t)³ at t=1

A: Given function: ft=t23-2t3 Find the value of given function at t=1

Q: Find ax dy x-2–1 given y = 2x3

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Q: , y = X = t+2 t+2,

A: The solution of the problem is given in the next step.

Q: Find y" from x =t +7, y = 6t -1

A: Answer and explanation is given below

Q: (a) x²y "-xy '+ y = Inx %3D

A: According to our guideline, We can solve only first question of multiple question.So here we solve…

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: 6. Find the domain of y = Vx+ 4x + 5x + 2 + Jxl-|x+1]

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Q: · (D² + 3D + 2)y = xsin 2x

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Q: a z = 4x³-6x²y²-y com x= 2sen(t) y=-3cos(t) e

A: #As per the guidelines we are entitled to solve one question at a time, please resubmit the other…

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

A: Given that: y=4x3+3x2

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

A: Given

Q: findthe solutionof the differenta eqration- dy 2X+y-) X 4X+2Y+5

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Q: Q1: 2ty 2t – (2 – In(t + 1)) y = 0 y (5) = 0 t2 +1

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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: х-2 y = at [-1,1] x²+1

A: The given problem is to find interpolating polynomial for the given function and interval using…

Q: z = xy³ – a²y, x = t² + 1, y = t2 – 1

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Q: 6. x = t and y = 3t – 2 for 0Sts4 %3D -

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Q: 2a V2ax 2ах f (x, у) dydx (a > 0) е. 2ах-х2

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Q: dy 9. x2-y = Jx2 – y². – y?.

A: Given:xdydx-y=x2-y2

Q: px + qy=z-a √x² + y² + z²

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Q: Then: f(x, y) = exy 2z3y fxxy 2 2z?y fxxz' XXZ 2z y Ofxyy= x2 Of- 2z3y2 fx² X

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Q: dy Find the general solution of xy + y² dr x2

A: According to our guideline, we can solve only first question of multiple question.So, here we solve…

Q: (x=1² +3t – 1 + 3t – ; at t=-2. t-2 y = t² +1

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Q: y = v1 - x2 from a = 0 to r = ;

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Q: v x +y = 2xy + 4x; at x = 1 and y = 3

A: Since you have asked multiple question As per our policy, we will solve the first question for you.…

Q: -3x2 F(x) = S*" t² dt %3D

A: TO EVALUATE THE FOLLOWING INTEGRAL F(x) ∫-x3x2 t2 dt FORMULA USED- ∫abxn dx = xn+1n+1 i.e substitue…

Q: (3x²y + 2ry +y) de + (x² + y³) dy = 0

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Q: dy Given y= x³In x, -is dx A 3x2In x B B 3x2in x+ x2 ( c) x2 D 3x2

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Q: d²y Find for y dx2 x-9 (Зx2-2х+5)

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

Q: Find the general solution of y" = 6y' – 9y where y is a function of x.

A: Given differential equation, y''=6y'-9y Find the general solution of the differential equation.

Q: dz Find from the equation x*y+ x z+ z² = 4 ax

A: We differentiate both sides with respect to x, considering z is a function of x.

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

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Q: Find: ydy-xdx (x2+y2) 0<x<1 & 0<y<1

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Q: y" (t) – y' (t) - 2y (t) = 12t - 6e2t; y (0) = 1; y' (0) = 0 |

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

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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: (D + 3D + 2)y = xsin 2x

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Q: (x = s² – t² y = s·t³ z = 2x – 5y,

A: See the attachment

Q: Find d²y/dx2 for the followi f) x2/3 + y2/3 = 1 %3D ³ g) x + y = 16

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Q: Calculate y(k)(0) for 0 ≤ k ≤ 5, where y = x4 + ax3 + bx2 + cx + d (with a, b, c, d the constants).

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

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