3. Z[ynd = 3z²-Z 212-18 %3D

Q: 2.Linean ectuation 4-L4y-3x)dX+5Xdy=o 5.

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Q: 1 7) Find the antiderivative: S 3x2-6x+12

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Q: Differentiate. y= In [(x + 4)(5x– 6)(3 – x)] d dy In ((x+ 4)(5x – 6)(3–x))) = |

A: Given: To find: The derivative of the given function.

Q: Find y': y = ez² + 3x² + e²e Oy = e + 3x ln x + e²ex Oy' = e + 3x²-1 Oy = e + 3x² In a Oy = e +…

A: Given y=e12x+3xe+e2e Given query is to find the derivative y'

Q: a) Y= ezx-e-zx €²x+e-2x

A: Given,   y=e2x-e-2xe2x+e-2x

Q: determine L−1[F].

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Q: 25y2-4 dy 415 S. 2/5

A: ∫254525y2-4y dy Put, y=25secθ Differentiating with respect to θ, we get ⇒dydθ=25secθ tanθ⇒dy=25secθ…

Q: Evaluate S S"(2y² + x)dædy

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Q: [d] If xz = yz and z - 0 then x = y

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Q: 3t y" – 3y' – 4y = e|variationof parameters

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Q: In z dz z4 e

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Q: [1] S(4x³ + x)V4x² + 1dx > [2] S(2x7/2 – vx)* d. [3] S V1+ 2sin3xcos3xdx

A: As per bartleby guidelines we are support to answer only 3 subparts of a question. This post…

Q: Compute ∆y and dy for y = x^2 − 4x when changes from x = 3 to x = 3.5.

A: Topic:- application of derivatives

Q: 9/ (4x’y² - 2xy)dx + (3xʻy* - x*)dy = o

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Q: X = e not inelude th degreo QUmbelin

A: The triangle is shown in diagram ,

Q: dy 2ty(y - 1) dt 3(1 + P):

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Q: 1. S+1)dy y2+4

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Q: S (x+Sy+wz ) dzoly dz 2 3x X-つ

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Q: y² + 5 dy J y²Cy² + 25)

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Q: 2 Find the Cerivative o3 a) y°(x+2)= c3

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Q: The following are the prices of shares of XYZ Co. Ltd. from Monday Price Day Thursday Price 200 160…

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Q: ydy 1. S- V25-16у* xdx 2. S- 9+x 2 dz 3. S- 2 +6z+10 xdx 4. S- 9+x

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Q: (4) (b) 10tsin(5t²- n/4)dt (4) (c) S 12(x³ + 2)ex¹+8x dx

A: We have to evaluate the integrals.

Q: .3 S(3 – e3*)²dx

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Q: L{t – e-3t} = + s-3 L{t – e-3t} = =-- I. II. s-3 L{t – e-3t} = +3 L{t – e-3t} = III. IV. %3D s+3

A: We know the Laplace transforms Ltn=n!sn+1, s>0 L ea t =1s-a, s>a Now, Lt-e-3t=Lt-Le-3t L t…

Q: 4". Sy' 8y Sx'e* y10)=8, y'l0).S X-

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Q: 8y dy e2y

A: topic - definite integral

Q: CV4-x2 4-x2-y2 1- o So Si s** ydzdydx Jx²+y2

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Q: 2 What is wrong with the equation dx =

A: Use the formula ∫xndx=xn+1n+1, to evaluate the indefinite integral ∫4x3dx.…

Q: 2 If "IF(x)dx=6 and frox)dx=7.50mm [rodr then f(x) dx = 5

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Q: S * x3 (2x+5-3Wx)dx 0월 18-52-28 100 +c 0 23 5 +5x³ 8x³ +15x² - 2 +c +c ○ 2x35x4 22 5분 28 +0 + 5 4 3

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Q: 1. S(x +5)5 dx 2. S(9+ x)² dx 3. S(2x +5)3 dx 4. S(3x + 5)²dx 5. S 2x V1 +x² dx 6. Sex+3 dx 7. S5e3x…

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Q: Consider the following IVP: y' = e; y(0) = 2

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Q: Z eXZ 4. xyz dydx dz

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Q: 3(1 + P) = 2ty(y³ – 1) dt %3D

A: Let us consider the differential equation dydt+P(x)y=Q(x)yn It is known as Bernoulli's equation…

Q: 1 S² = y e2y dy

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Q: dy 1+y+1

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Q: + 4 oly +6y =0 dt dy +2 -6x=6

A: Introduction:Simultaneous equations are those in which the derivatives of two or more dependent…

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

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Q: S(6 + 6y – y²) dy

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Q: 6) y = e *(x* – 5) dy A) dx 5x² 10x + 4x3 = 21(5e* + 2x²) dy 5x2 B) = e* · 10x · 4x³ + e³* · 10x ·…

A: Let h(x) = f(g(x)) for all x, then by chain rule   h'(x)=f'(g(x))g'(x)  Also if h(x)= u(x)v(x)  Then…

Q: 1 y2e- dy 7 صواب ihi

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Q: Find (5x - x²)e* dx O(x2 -5x)e-x-(2x - 5)e¯X – 2e-*+c O (5x-x2)e*- (5 – 2x)e* +2e* O (x2-5x)e*- (2x…

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Q: dx + 6x y- dy 1 y = (x – a²C)³ (y – y²C)³ Option 1 Option 2 1 1 (y+ y²C)³ (x + x²C)³ Option 3 Option…

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Q: 5) SOLVE dy _ yz %3D x2

A: A differential equation is an equation in x,y and derivatives of y. An ordinary differential…

Q: 4. V21+4:-z dz

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Q: -1 x-x2 dx -8 2도 1423 1521 22 20 Option 1 Option 2 1425 1523 22 20 OOption 3 Option 4 None of the…

A: Given problem:-

Q: 19) If y- find the value of yl.3y. 3' A) 3. C) 1 B) 0 D) 3

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.