z(z² 2). 9. y Ans. dy -1 dz (z + 7)* dy 1 Ans. dz (4 z) 2y 11. 12 ong b Ey - 2 - 3z 3z - 1 Ans. y = -3 dy 17 2z + 5

Q: The standard form of 3dy – xydx = 3y³e¹x/³ by Bernoulli's equation is: dx A d 2=3e dy ху B D…

A: Solution : Given that

Q: Q2/ If y= u3-1, u=2X Find dyldx. * dy dy du "= 3u2 * 2= 6(2X)2 =24X a- dx du dx Option 1 none of the…

A: Given that , y=u3-1 u=2x dydx=?

Q: 1-² dx dy dz se ³ 1 xyz 2-fff(x+y+z)dy dx dz TL 3-fff₂y sinz dx dy dz 6 -2

A: As per Bartleby guidelines for more than one question asked only one is to be answered please upload…

Q: Inx+ 1 dy If y = then %3D 2x3 - 3x' will be dx (2x – 3x) + 1) – (In x + 1)(6x² – 3) А. (2x³ – 3x)² -…

A: Use the formula of differentiation of fraction of Two functions in same variable.

Q: /1- (z² + y²) dz dy dæ ) Evaluate

A:

Q: dy ху+3x-у-3 7. Ans: y-x+In y+3, %3D = C dx ху-2х+4у-8

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Q: dy (2) Find at x =-1 if y = u³ + 5u – 4 and u = x2 + x dx

A:

Q: B) dy = 8xex2. 9) y = e4x² + x A) dy = 8xe2x + 1 dx B) dy = 8xex2 + 1 %3| C) dy = 8xe + 1 D) dy -…

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Q: x²V4x +1 dy then dx If y = In (x³ + 5)3

A:

Q: If xy² + x 4+x + y = In x-y dy then dx at y = 0 is Select one: O a. -2/3 O b. -6/7 O c. -7/8 O d.…

A: Differentiate wrt x

Q: 4.Jy2-プdy

A:

Q: 8. Jydx + (1+ x)dy = 0,,when x = 1, y = 4

A: Differentiable equation can be solved separating the variables on each side and then integrating…

Q: 1 [ (2 -y - VE) dy 2 – y – 0. 1 | (2-y (2 – y – V9) dy 0, 2 | (x² – (2 – æ)) dæ - 2 [ (2² – (2 – a))…

A:

Q: 6- Find ify dy t2 and t = V2x +1 dx t2+1 dy A): 2 dx 4(x-1)2 dy B) dx 2 2(x-1) dy C) dx (x-1)2

A: We can do this by chain rule or by putting value of t in y y=t2t2+1put…

Q: C/ Answer two only: dy dy 1- y= eV1+5x? the dx 3- y= 2r° +3 , x =, he .(using chain rule). dx dy 2-…

A:

Q: Find dy/dx if y = u5 - 2u3 + 8 and u = x2 + 1.

A: Given function are: y=u5-2u3+8......(1) u=x2+1......(2) The objective is to find the value of dydx.

Q: 36. Using the approximation dy dy h dr * Yn+1- y. and that dr 1, y = 2 when r 0. Then, y A h- 2 h+ 2…

A: Please see the answer below.

Q: -2dх 38. y-2dx dy er e2x + 1' УО) %3D 1

A:

Q: 4. Suppose that z = x³y, x= t², and y = t³, find . dt = 12t11 dt 11t10 b) = 10t° dt d) = 9t® dt

A: This question is related to differentiation, We will solve it using given information.

Q: In (A) y = 3" (B) y = 3* (C) y = -3* (D) y = -3*x (E) y = 3* – 1 (F) y = 3*-1 (G) y = 31-x (H) y = 1…

A: Assuming  f(x) as a exponential function Then by shiphting

Q: z = In (VT" + y") If With n e N, n > 2, Then the result of 2 (dz dy dz n Corresponds to: "-1 + y"-1…

A:

Q: dy de =1+eV-z+5 O e*y+5=x+c O ey+5=x+c O y-5x+c O exy-5=x+c

A: given differential equation dydx=1+ey-x+5 find the solution of the differential equation

Q: re' dy + +1 dr =0 O (y – 1) e + + In z = C 2. O-(y+1) e + Ine =C 2 O (1- y) e + 1. O 2y - e + +In=C

A: To solve given differential equation

Q: dy Q1/ Find dx 1. if y = u and u 4x2-2x +5. %3D 2. y = (x2 + 4)2(2x3- 1)3 %3D 3. xy + x- 2y- 1 = 0…

A:

Q: (y? + xy*)dx + (5y² – xy+ y* sin y) dy = 0 - Let M = y? + xy³ and N = 5y² – xy + y³ sin y ƏM 9. =?

A: We have to choose the correct option from the given options according to the given information

Q: Y 30 ΨΥ Ỉ2 2 47 13 23 24 με χ ΕΙΝΑΙ Fino η Exy. ἐκ ἔγ In ex² - (Ex)^ in [y- (fy) th nexy- έχτι…

A: Given information: X Y X^2 Y^2 XY 27 30 729 900 810 44 19 1936 361 836 32 24 1024 576 768…

Q: 5. Evaluateſ, x²y dx + xy² dy where C is given by: r(t) - 3t v(t) – et 0<t< 1

A:

Q: dy (3) If y = | (t – 1)²dt for x > 0, then compute dz In z

A: fundamental calculus theorem 2 states that if f is continuous on [a, b], then  ∫abf(x)dx=F(b)-F(a)…

Q: ∫C  z2 / (z2 + 4) dz with C defined as z(t) = 2i + 2eit and 0 ≤ t ≤ 2π

A:

Q: Show that y +4 dy = 4 In lyl – 3 In |y + 1| + C y2 + y

A: To Prove:  ∫y+4y2+ydy=4 lny-3 lny+1+C

Q: d²y dy + 3x+y = 4sin (In(x)) dx²

A: Given Euler differential equation is: x2y''+3xy'+y=4sin(ln(x)) Let us take x=ez Replace:…

Q: 2. [e2y ycos (xy)| dx + 2xe2y [2we?y xcos (xy) + 2y dy = 0 -

A: The solution is given as

Q: Q5. Evaluate ſ^₂ ¹¹ xy dx dy. ry+1 y²

A:

Q: dw If w = x2y sinz - 3zey, find dz 6. O a. dw =x?y cosz - 3exy dz O b. dw =2x2y cosz- exy dz O c. dw…

A: Find the partial derivative of w  with respect to z

Q: - 3-z2-y 2. Evaluate L* L z dz dy dx -5+x²+y²

A:

Q: 5. y' + 2y = 0, when x = 0, y = 2 %3D Ans. y = 2 e-2x %3D dy 6. xy +2 y– x - 2 ху — Зу+х-3 dx (у -…

A:

Q: If the substitution m = 2x - y was applied to the DE: (2x – y+1) dy + e2-dx = 0, the resulting DE…

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Q: dy — 2х — сosX + e-2х dx 2 TT 1. Given that and y = 1 when x = 5. Express y completely in 2 terms of…

A: Topic - differential equation

Q: - If y = u – 4u and u = = 3x + r, then dy с. dr 1 dy а. dx 12x3 + 1 12x3 + 1 3u? 4 dy (3u² – 4)(12r³…

A:

Q: 2y4 y3 – y2 + y – 1 dy = y² + 2y + In ly – 1| -in ly2 + 1| - y +C

A:

Q: [ a(x+y) - xty]dy = (x+xy²- 2y +3)d« when x-1, yal 3. %3D (9xy - 2y²) dx - ( 6x²_ xy) dy =0 4.

A: I have authority to answer one question only, if you want another question to be solved then upload…

Q: 4. Find dy and Ay for y = 3VT-1+2x at r = 2 with dr = Ar = 0.2. %3D

A: The given equation is y=3x-1+2x. Given that x=2, dx=△x=0.2. Now,…

Q: 5. ydx - (x +3y')dy = 0 Ans. x = 6y In C

A:

Q: Q6/ If Y= 5u3 where X=u2, u=vx. find dyldx. * dy_ dy dx_ 15u2 dx du' du dy ,dx 15u? du' du 15u 15x…

A: Topic- derivatives

Q: dy given (6 x – y)² – 5 y = 2. da Find | - dy 72 a 12 y a) О dx 12 x 2 y-5 dy 2 a 12 y - b) O %3D dx…

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Q: _8. If y = (2x + 7)², then what is ? dx а. dx dy 2(2x + 7) C. dx dy = 2 %3D dy dy b. dx = 4x d. = 8x…

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Q: (b) If z = 9t²e 4t, find 4 dz dt

A: Given.

Q: 1. y' = xy ; xydx – dy = 0 2. y' = xy ; xdx -dy = 0 3. y' = xy + 1 ; (xy + 1)dx - dy = 0 E) dx – dy…

A: