// (3x + 4y)dA where Find D D = {(x, y) | x² + y² < 4, x > 0}

Q: dy y² tion + dx x² है || Y 8

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

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Q: d²y dy – 4 + 4y = e2t.t dt2 dt

A: our objective is to solve the differential equation

Q: b. min f (x, y) = 3x² – y² s.t. 2х — 4у 3D —11

A: Minimum value of function is determined using lagrange multiplier and its value is -33/4.

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

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

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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. zy if y + x² – 3xz = 222

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Q: y = x(2x+1), y" y = (4x − 3)¹/²2, d³ y dx³

A: Topic:- derivatives  Note :- as per our guideline if more than one question uploaded than only first…

Q: r/64–x² r61-x²-y² x dz dy dx -67+x²+y²

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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: Find d2y/dx2 implicitly in terms of x and y.

A: To findd2ydx2

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

A: Given

Q: max z = 2x + 8y %3D s.t 3x + 9y 12 х, у > 0

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Q: 3. (D2 + 2D + 1)y = 0; when x = 0, y = 1, Dy = - 1.

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

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Q: y² + 5 dy J y²Cy² + 25)

A: Given problem:-

Q: (3x + y5)dy – ydx = 0 %3D -

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Q: Find dy if y= (4x+3)/(x2+6)

A: Quotient rule for derivative: ddxuv=vdu-udvv2

Q: Q3:A/ Find: dy dy y 2 Vy (1 + Vý)² yV4y? – 1 |

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Q: Find dy. y=5ln(3x+x4) dy=

A: To determine the derivative of the function.

Q: ๆ ³₁₂₁ (4x²y — z³) dz dy dx -2 J1

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Q: Find dydx for…

A: the given equation of the curve is: y3+y2-5y-x2+4=0 we have to find the value of dydx

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

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Q: dy If dz 3x - 3 and y(0) = 8, then y(1) %3D ---

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Q: dydx x² +y²

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Q: d³y of y = (3x*-5)(2x³+9x-6) Determine the %3D dx3 7x5

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Q: Find of z = 2x° 5xy" + x¯ y dy2 -10ху + 3x? у? = -10y + 6xy²

A: To find ∂2z∂y2 of z = 2x3-5xy2+x2y3

Q: 2. (D2 + 3D)y = -18x: v = 0. Dy = 5 when x = 0

A: Given differential equation is  D2+3Dy=-18x  and the given conditions are y=0, Dy=5 when x=0 find…

Q: F(x,y) = -41² - 2xy-4y² +z+y.

A: Follow the procedure given below.

Q: Н. W.: -1/3 6dx 2. V9x2+ 1 c2/3 dy

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

Q: (у-3) dy y2-6y+1

A: To evaluate the integral: ∫(y-3)y2-6y+1dy Solution: ∫(y-3)y2-6y+1dy…

Q: 29. t²y" - 4ty' +6y=0, t>0; y₁(t) = t²

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

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Q: Find Vy where = (x² + y² + z²) e¯¯ √√√x² + y² + z ²

A: Given :ψ=x2+y2+z2e-x2+y2+z2

Q: Vy² – 25 dy y3

A: SINCE YOU HAVE ASKED MULTIPLE QUESTIONS IN SINGLE REQUEST, WE WILL BE ANSWERING ONLY THE FIRST…

Q: Suppose that 3x² - y² = t² and y=tsin 0. Find dy ().-0 (27). and X

A: Given 3x2-y2=t2 and y=tsinθ

Q: y" – 10y' + 34y = 3x2 + x – 1 || | (D² – 10D + 34)y = -cos3x

A: 1-D-1 = 1+D+D2+D3+.... Note : As per our Guidelines, we are supposed to answer first question.

Q: d'y dx2 (3y -1) 24y If y' -y = 2x prove that

A: Solution: The objective is to find the double derivative of the given function

Q: dy y2+1

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Q: (x = s² – t² y = s·t³ z = 2x – 5y,

A: See the attachment

Q: 41 82x-x2 9V x²+y? dydx =

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Q: Find DF of fcx,y)=x²e° at the point (-2,0)-

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Q: d²y Find dy 34 y3 %3D こX+

A: Answer

Q: Q2 Find2 of y = 4x/x+ vã at x=1? %3D

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Q: 523 + 222 – 5 y = dy then dz 3x + 2

A: Consider the provided equation, y=5x3+2x2-53x2+2 Find the derivative of the equation with respect to…

Q: Find formulas for dy and Ay if y = x² – 7x + 3.

A: To give the formula dy = f'(x) dx and    ∆y = f(x+∆x) -f(x)

Q: dx Vx²-4x-7 7. dy y2-8y+5

A:

Polynomials

Try substituting 1. You will get 6 and not 0. Try other real values also. What About -2? Let us check.