dy , Suppose z and y are variables that satisfy the equation r² – y³ = 12. What is dr

Q: If (x, y)= x²y+e* , find; d. y е. b. $, с. Ф Q.4 (1)

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Q: If y(x) is a solution of xy" +(1-x)y' +6y = 0, find the value of y'(2). %3D

A: Given differential equation is xy'' +1-xy'+6y=0 -----(1) Also,  y'' +1-xxy'+6xy=0 Here,  limx→0…

Q: For the equation Mdx+Ndy=0, if both M and N follows that f(Ax,\y)=^k f(x,y), the equation is A.…

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Q: Use the equations to find dz/ðx and əz/ðy. x2 + 8y? + 9z2 = 1 Əz ax az ду II II

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Q: Find a solution of x dy =y?-y that pases du Through indicated points

A: For the given problem, below is the solution.

Q: What is the solution (ry – r) dr + (x²y + y) dy = 0 when 2 and y = 1

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Q: Show by direct substitution that is a solution of y" +xy=0_ _and write the general solution.

A: Given that, y=xj1323x12 And the given differential equation is, y''+xy=0...1 The solving by power…

Q: Let y(x) = c1 + c2x + C3 et is a general solution for D. y" + ay' + by +cy 0, Find the value of a?

A: To answer the given question, we form a differential equation from given general solution.

Q: Use the equations to find dz/əx and əz/əy. x2 + 4y2 + 9z? = 1 əz ax əz ду II

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Q: Find the particular solution to D²y – 6Dy + 9y = e3x – ex when x = 0, y =y' = - 3 %3D

A: For given differential equation we have to find particular solution.

Q: Given that d²y 2. +y =0. dx2 Show that y = x is not Solution a

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Q: a) Are Y1 and Y2 independent? b) Find V(Y1 – 2Y2), if we know that E(Y,) = E(Y 2) =}.

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Q: Let y1, Y2 be two independent solutions of (t 1)y"- ty' +y = 0. If W(y1, Y2)(2) = e2, then W(y1,…

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Q: y"-8y' + 16y 0; Y, = et e JP(x) dx xp- (5) as instructed, to find a second solution y,(x).

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Q: 4) Find dy where r and y are related by the equation r?y + r³ + 2y? = 5y.

A: Given  x2y+x3+2y2=5y Apply power rule to take derivative We know that , derivative of x is 1  and…

Q: Solve the given DE. (D³ + D² + D+ 1) y = 0 ; y (0) = 2, y' (0) = 2, y" (0) = -4

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Q: dx Cane:2e-25x

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Q: Q2) If y(0) = 0 and y'(0) = 0, ƒ (t) = e*t, %3D 1 y(t) = (D + 3)(D + 2)(D + 1)ƒ (t), determine y(t).…

A: Here first calculate differential part.

Q: If y = 3x + 2x² + 4x – 5, 4х — 5, dy find at x = 1. da? a. 24 b. 26 С. 22 d. None

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Q: Use variation of parameters to find the particular solution to y'" – 7y' + 12y = 3e Y(t) =…

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Q: If yo is the solution of the equations xy' + 3y = x, y(1) = 2, %3D determine the value of yo(2).

A: Given a first-order differential equation,                             .....(1) condition  y(1)=2

Q: If QR what is the value of y? 11y + 45 and SU = -5y + 33, T. S R U It

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Q: Determine the solution to the I.V.P. y"+7y'+12y=2le",y(0)=,,y'(0)=-10 %3D vious Next

A: Please find attachment for the details solution

Q: dy = Solve 2xy r x2 + y? given that y = 0 at a = 1 %3D

A: To find particular solution of D.E.

Q: The general solution of the DE x?y" + xy' – 9y = 0 where y(1) = 2 and y'(1) = 0 is %3D

A: Given differential equation: x2y''+xy'-9y=0 wherey1=2 and y'1=0

Q: If y = ex, then y equals 2x (A - 2y В +3 C) none of the given choices - 2x D E

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Q: If f(x, y) = C, CE R, find y" d²y dx²¹

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Q: SUppOrE THAt y VEIES DIRECTLY WITH X ANO y =9' WHEN X = 18 X HUIM WRITE A DIRECT RAATES. VAQMOW…

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Q: If y* = ex , then y equals 2x (A B none of the given choices – 2x y3 - 2y D +3 2y E

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Q: By making the change of variables u = 2, v = x, find the general solution of yfyy +fyx + fy = 1.

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Q: Observe that y = x is a particular solution of the equation %3D 2x²y" + xy' – y = 0 and find the…

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Q: What is the particular solution if y(1)=D0? 1/2 xy = y+ (a² + y³)2

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Q: Evaluate | (r + y)ds, c : x 3t, y = - 3t + 3, for 0 <t< 3.

A: Given: ∫C(x+y)ds, C: x=3t, y=-3t+3, for 0≤t≤3

Q: b) Show that if y(t) is a solution of the problem y" +e*y + y = 0, y(0) = 1, y'(0) = 2, %3D then…

A: Given y''+e-ty'+y=0, y0=0, y'0=2

Q: Find r, if b = 0.8 and b, xy = 0.46. %3D yX

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Q: If y, =e", y2 =te are solutions to y"+b y' +c y = 0, find the values of b and c.

A: Given: y''+by'+cy=0y1=e4t ,y2=te4t

Q: Show by direct substitution that is a solution of y" +xy=0 and write the general solution.

A: Given :

Q: If y = f(x) is the solution of æy' + 13y – axy? = 0, f(1) = 12/a, where a + 0 is a re а, number,…

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

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

Q: 設+xy=X, y(の)=-6

A: see 2nd step for this question's solution.

Q: (b) dr(x -y) dy, where y, = Va? – x?

A: Multiple integrals

Q: The equation r = 3tanosece ,expressed in rectamgular coor dinates is given by: (a) y² = 3x (b)V3x =…

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Q: ,2 y² e2y dy = e2y 2 (y² y + C 4 2

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Q: d'y If y = x° + 5x, then dx? is %3D а. бх + 5 b. 6x с. О d. None е. 6

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Q: Show that y = c1ex + c2e-x + c e + 3 is a solution of y ||| -2y | | - and | + 2y = 6 (justify).

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Q: Consider the following IVP: y" + 3y' + 2y = 12x2; y(0) = a, y'(0) = b Find the solution.

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Q: If y = ex , then y' equals (A none of the given choices - 2y x3 2x 2y D 2x E

A: Please refer the attached image for complete solution. THANK YOU.

Q: V = yz + zx?, p = x³y²z

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Q: y? dy 4-7 2.

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