3 2(x-1) + If y = Vx? – 2x then y' 3Vx2-2x F

Q: (c) | Vtan(x) sec (x)dx 3

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Q: 5- dy/dt = y²(y+1)(y-3), -∞<Yo<∞

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Q: + 1 =2e- dy

A: Given, Can be rewritten as

Q: How come it is 20y and not 20y^2/2 after integrating?

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Q: Vx 3 1- evNīdy dx - 3 y3 e*y dx dy

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Q: 3 9 dx dt -1 -3 with x(0) : 4 Give your solution in real form. X1 = X2 = 2. II

A: The objective is to solve the differential equation:

Q: 3. II Azy'dz dy = 2y°(3² – 1)dy | 2y (y? – 1)dy 1

A: Given that a double integration .We use general  property of integration to solve this integration.…

Q: 6. (6x – 3y + 2) dx - ( 2x - y– 1) dy = 0 ans. 3x - y + C = 5 In | 2x - y + 4|

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Q: 29, + 16y=0 geoJ = 2, go)= -2 2. 31, dy dy -54 =0 dt

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Q: 2. (3x-y-4)dy -(x+y-4)dx=o

A: Given :

Q: 2 dx + ( 2x-y+3) dy = 0 ans. y + C = - In |2y-y+4|

A: See the details solution in below

Q: Q4/ 1- Evaluate: f/2fy sinx dy dx ди 2- If u = x² + ey² ,x= sin 2t , y = cost² find at

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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))…

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Q: (x²-xy-y²\ (x2-ху-у?) dy = 0 dx + r2-v3

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Q: (a) (Ex) ((Ax --> Bd) --> Ky) (b) (Ex) ~ (Dx v Cy) (c) -(x) (Dy --> (Hx v ~Ga))

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Q: 2x+2 dx. 5. x2-2x+1 dy 6. 5. if y = (1+ x²)etan-1x

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Q: Evaluate the integrals

A: The given integration is: ∫03∫09-x2∫09-x2 dz dy dx Here first to solve the inside integration with…

Q: 2.Find the particular solution of y (9x-2y) dx -x (6x-y) dy=0., when x=1, y=1. Let x=vy

A: Find out the particular solution.

Q: 2²ye+v°-²dx dy dz 1 -1

A: We have to calculate the integral.

Q: Solve the particular solution of 3y(x^2 - 1)dx +(x^3 + 8y - 3x)dy = 0; when x = 0, y = 1

A: The given differential equation is 3yx2-1dx+x3+8y-3xdy=0. The initial condition is x=0 when y=1. The…

Q: find dy/dx 3x² +5y'x² +4/y, a) x² +4x,/y-5y² = 3 (ans.: 2x 10x'y- Jy

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Q: 33 2Vx- f(x) = T sin sin 2x + Ve2x + 2x – In e, x + 1 - 1-x (1–3t)5(t³-8) alt) t # 2

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Q: dy 5. S: y(1-Vy)2

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Q: dx. J x² + 2x + 5 x+1 11 arctan x+1 11 ;+ 2x – In [/r² + 2x + S- *+ 2x + In Vx? + 2x +5+, arctan 2 2…

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Q: (2t – 3)·e -t²+3t dt 3 2/Inx dx . X (2у-3)12

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Q: 7. 2r tan y dx + sec² y dy = 0

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Q: sin(2t + ) dt JT 2 e2t-3 -3 4 e3 7 7 64e3 7 8. 5 4 4

A: Proceed as shown

Q: d x dt 2+ + 3x + 5y. = LY dt -3Y-5X ex

A:

Q: 23. (4y + 2t – 5) dt + (6y + 4t – 1) dy = 0, y(-1) = 2

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Q: (2x-3y+6)dx-(4x-6y+2)dy=0 in Linear two variables with POI

A: Here, the given differential equation is: (2x-3y+6)dx-(4x-6y+2)dy=0 The equation can be written as:…

Q: (3– 3cos5x)} (3x² +2x-7)² (e - sinx +3x) y= Find dy/dx if

A: That's computational, take a careful look.

Q: 1. (2x -х-у)dx- хdy - 0; y(1) -о

A: Given that: (2x2-x-y)dx-xdy=0; y(1)=0

Q: Solve integration by (udv) T/2 DS Š X cos(x) dx 2) { X cos (ux) dx 7/2

A:

Q: By differentiating x² – y² = 1 implicitly, show that d²y | dx² ||

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Q: 1,- X73X+2 dx (x+リ) Izafhinx dx Ax. Iォfュース alx dx X43X+2 X+1

A: Since, you have posted multiple, we will solve only first part. If you want solution of other…

Q: 3. a) If y = 6x - 5x +7x +2x – x+10, find dy at (2,3) i. dx d'y il. -at (1,-5)

A: See the attachment

Q: 4x cosex²x+ 5 1 4 secxtan x+ dx. 4. Integrate Vx 3

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Q: 3) Find d²y/dx² at the point (1, 1), if x6 + y6 = 2.

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Q: 1. If f(x, y) = sin(4x-2y)+ln(x²-2y) find fy fyx

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Q: sin(3z+z²) Find y' for y = (6 – 2*)3

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Q: 1-fd dydx R = {0,1} * {2,5} y2 2-S y2 (1–5x)2 dxdy R = {0,1} * {0,2}

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Q: 3. (6x + y²) dx + 2x - 3y) dy = 0. ANS. 3x + xy² ya:

A: Here we have to solve the differential equation.

Q: /25-x2 V25-x2 -y2 1 dz dy dx -/25–x² -V25-x² -y²

A:

Q: What is the I.F of (x^2y^3+2y)dx+(2x-2x^3y^2)dy=0?

A: Find the integrating factor

Q: 3. Integrate! 12e-0.21 а) -dt b) 6r 3,2 Se041 dr dx c) f- x. V1+ In 3x?

A:

Q: (b) Integrate x-³e-l/a², dx

A: Here we can find the answer as below.

Q: 1 dz -÷z³ = t² + 3t – 2 dt 3 z2 -

A: Differential equations and their type

Q: 9) (x- y°-Ay-1) dx t 2x (x4 y +2)dy =o

A: As we know that the differential equation Mdx+Ndy=0 is exact, If ∂M∂y=∂N∂x. The solution is:…