[y(8y² -5)dy 4y* -5y? +5 1.

Q: 3. f(x, y) = (3x - 5y)2 + e4x In(4y – 9) + %3D 135 x4

A: We know, ddxxn=nx(n-1)  , for any real number n. ddxln(x)=1x

Q: -3dy 6. zy2+14y+70

A:

Q: d²y 54. Let y = 4r+2r+l_find CL)

A: To find the double derivative of below expression.

Q: Find d²y if y =x² +3x-7 and x=2t+1. dt?

A: y=x2+3x-7 and x=2t+1

Q: If SeF dr = [c(-5x + 3y² ) dx + (x³y) dy, what is F? %3D F =

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Q: of Chal) D x24 6x -2:0 ent

A: Solve x2+5x-2=0

Q: Find ax dy x-2–1 given y = 2x3

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Q: ー2 f Cx.y)=In Cx Zp

A: Please refer to the image below

Q: y'(t) = In(y- 3) %3D

A:

Q: 2. x y-3xy = 4x + y+1 at (0, - 1)

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Q: y" + ay' t sy = g e-2^ + 8 %3D ylo) ay'6o) =

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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: 6. S Se(x² + y³)drdy, wherein B = {(x, y) E R²; 1< x² + y² < 4}

A:

Q: Evaluate..(x+.2.y.)dA..„.where.D.is.theregron. sunded. by.the.paradoolas.yz2x.and.y..l+x. 2 2

A:

Q: Not sure how to start problem

A: Given functions are We find g(f(x)) by replacing x by f(x) in g(x)

Q: 4yy" + 2y' = 0 = y' =? A) y'= -In B) y' = In c) y' = 2n(cy) D) y' =-In E) = 4 1n

A: Given that 4yy"+2y'=0

Q: Find dy/d 5x²+xy+ N9 - Say %3D =D0

A:

Q: If X =V1-t and y= - 3t +t°, what is y' ? O 6(? – 1) /1- O -3 (t? - 1) /1-t %3D 0-6 (t-1)(t + 1) /1-t…

A: x=1-t and y=-3t+t3

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

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Q: Q5/ find y', y=In(Inx) * O y'= 1/( x-2x)*(2x)=1 O y = 1/( x-2x)*(2x)=2 none of the above

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Q: +2x (D³ – 4D’D'+ 5DD" - 2D") z=e** + Vy +x.

A: Given PDE is D3-4D2D'+5DD'2-2D'3z=ey+2x+y+x We can write it as D-D'2D-2D'z=ey+2x+y+x             (1)…

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

A:

Q: Find the domain of y = 3x+3. %3D X S-1 O x 2 -1 O x > 1

A: NOTE: Refresh your page if you can't see any equations. . as we know square roots of a negative…

Q: Let f(x,y) = 10x^3y^4+ 21xy^2 Find ?yyy

A:

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

A: To determine the derivative of the function.

Q: EX. Evaluate the JJ(X*+2xy+y") dydx when step size of x = 0-2 and step Size of y=o.5?

A: Given: ∫01∫02x2+2xy+y2dydx with a step size of x=0.2 and y=0.5.

Q: Find the general solution to the 2nd order ODE: y" + 4y' + 4y = √xe -2x

A: To find the general solution to the given 2nd order ODE.y''+4y'+4y=xe-2x

Q: Find the domain of y = vx+6. %3D 12. O x 2 6 O x > 6 1/6

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Q: O': Find the general yy' – 2y² = e²

A: A first order Bernoulli ordinary differential equation is of the form dydx+pxy=qxyn Where p(x) and…

Q: a.) = y° (4 – y²) - b.) y' = y In(y+ 2) %3D c.) = (ye" – 9y)/e" -

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Q: 32. In y = 2y² - x; (2, 1)

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Q: Find The Pollowrng in tograls:- Excersises 4 ( 2x + 6y x*) dy de (2 (ay + 29) dë dy + +) dy da x+4

A: As per our Guidelines we can solve maximum 3 question as per request , otherwise we solve one…

Q: - Q3): If xfx + yfy = nf show that x²fxx + 2xyfxy + y² fyy = n(n − 1)f

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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: A. Find dy 1. y = In V3x²- 9x +1

A:

Q: (18) y "+9y '= sec² 2x %3D (19) y "'+6y "–14y'–104y = -11 le*

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Q: = (y² – z² +3yz – 2x of the following is/a

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

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Q: ral of the d D- 1)y is

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Q: yesin 3y* dy dy 5. csc 6y

A: The question is a little incorrect. I have modified the question a bit: the denominator should be:…

Q: Evaluate /, a Te dydx y2 2 JJ4X-x² 32 dydx (x²+y²)' V4x-x? O 4 In(v2 – 1) – 4+7y/2 3 4 In(v2 + 1) –…

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Q: f Lan 2X e *3 of +sec2X Pinel dy o

A:

Q: :- (x.y)=3€XY, compute ay 6x %3D

A: As we know that the chain rule: fgx'=f'gx·g'x The product rule: f·g'=f'·g+f·g' a). Given: fx,y=3e2xy…

Q: What is the discriminant of the PDE?    4d2/dy2=-3du/dx-4u

A: the discriminant of the PDE is :

Q: b. xy--2×y- ヴり C. 2x- xy - zy +> - xyy'+ 2xy'; when x 1 when X = 0, y-1 19=1

A:

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 dy if x2 + 6xy = 3y2

A: Given: x2+6xy=3y2 If function if f(y) then differentiation w.r.t x is ddxf(y)=ddyf(y)dydx

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: 18.t2y′′−4ty′+6y=0,t&gt;0;y1(t)=t2

A: