($4y - 7y–12 dy. y' +y? - 6y Q.4 Evaluate

Q: 3. f 3/2 y dydx (I wz dx dy dz. 4.

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Q: S dy(t) = y(t) = - iw ſe-iwt dt.

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Q: Evaluate the integrals

A: ∫01∫0x2∫0x+y2x-y-z dz dy dx

Q: dy + 3x?y = x', x?, y(0) = 2. %3D dx

A: The given differential equation is  dy/dx + 3x2y = x2 y(0) = 2

Q: an expiicit solu 'V1-y dx - V1- x² dy = 0; y(0): O 4+3/5 8 O 4-3/5 8 O 4-/5 O 4+ /5 2.

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Q: dy_ 1-y dx V1-x? V1-x' +/1-y? = a(x - y), then show that %3D

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Q: d?y dy 2- 8y = 8x? + 20x + 2, at y(0) = 0 and y(0) = -8 dx? dx

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Q: dr -x = 4y, dt MOUTM dy dt +x= y+3e', tt 0, r 3, and y = 0. %3D

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Q: Q) Find y" + 3y 5y at x-5 where y = xsin(1/cscx))

A: NOTE- AS THE SECOND QUESTION PICTURE IS NOT CLEAR SO I AHVE DONE ONLY FIRST QUESTION. IF YOU WANT…

Q: (b) y = u4 and u = 9x2 – x + 7 dy du 4u³ ,3 du 18x – 1 dx dy dx &x(9x² – x + 7)³ × II

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Q: dy Find for y = dr dy dr || r J√3 + 0 3 + 4t2 dt.

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Q: d'y dt? dy - +6y = 21° –t +3 ; y(0)=1, dy -(0) = 2 dt -5 %3| dt

A: At first, we have to find the complete primitive (C.F.) and then we find the particular integral…

Q: dy Q 3-Find dt if y+ 4x? = 7, x+-3 %3D

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Q: Find y': y = arctan(e2x) 2e2x y 1– e4x? 2e2x y = 1 – e4x %3D 2e2x y 1 + e4x %3D 2e2x y 1 + e4x2

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Q: dy +y de : 2 et dx Arowar 1- ye" (c -x*) 1= yet (c -x*) %3D

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Q: Evauate: |(*+xy) dx+ Cy- xy)dy; C: the x-axis from the origin to 2,0) and then line x-2 from (2,07…

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Q: 1. xdy y(1+ Iny- In x) dx

A: Note:-  as per our guidelines we are supposed to answer only one question. Kindly repost other…

Q: (2y-x)(dy/dx) = 2x + y, given that y = 3 and  when x = 2 Homogeneous equations

A: Solve the following problem by substitution.

Q: y" + 4y = cos(t−3)+4t, y(3)=0_y (3) = 7

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Q: . (r+ 4y – 8)dx – (2r + 8y + 6)dy = 0 Answer": 36(y – 2) + 22ln(-3x – 12y + 13) = ( %3D う 」フ ょうん。

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Q: dy y? – 1 y(2) = 2 %3D dx x2 – 1' -

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Q: dy If x = 3t2, y = t³ then %3D dx II

A: Here we find out the dy/dx

Q: @ yーJ=ex 12 y3=

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Q: 4 J4- y ktx dy S[S( x, y) dA = [] 3 R 0 2- 2 2

A: Consider the given expression, ∬Rfx,ydA=∫04∫2-y24-yx2-x33dxdy This suggests that the region spans…

Q: d'y dy 4+y =r²-21 +3 dt? dt

A: We will calculate CF and PI separately then we will add them.

Q: 2) Determine dz/dx and dz/dy for z* – y? + x² = 6x²y³z? %3D

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Q: dy dx What is y(2)? Suppose = 6x² + 2x − 3 and y(0) = 4. - oy(2) = 14 oy(2) = 16 oy(2) = 18 oy(2) =…

A: The answer is given below:

Q: dt2 d²y e. ++ 4y = 8t – 10, y(0) = 1, y'(0) = 7 %3D %3D %3D

A: As you post multiple questions According to the guideline I only solve the first problem. Please…

Q: •1 p3y IT Vx+y dx dy JO JO

A: Given: I=∫01∫03yx+ydxdy    ...1 Let, x+y=uSo,ddxx+y=ddxuddxx+ddxy=dudx1x1-1+0=dudx1=dudxdu=dx For…

Q: d?y dx2y =0 with initial conditions y(0) = yo and y - 0 as x oo,

A: We have to find the solution of the following differential equation.

Q: dy If y = x (e* - 1), then %3D 6. dx

A: Given: y=x^2 ((e^ x)-1) To determine: d y/dx

Q: dy =r-ky, y(0) = y, dt

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Q: In(y) dy V. 6.

A: This is a problem related to integral by parts. Based on the general formula of integral by parts we…

Q: Solve the IVP for y(æ): dy + dr y = 19y", y(1) = 1 y(z) =

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Q: -+y? сos(2t) %3D 0 ; y(0) = 1 dt

A: Given dydt+y2cos2t=0   y0=1

Q: dy If y = 4x3 + 5x and dX dt 2, find Y when x = 3. dt dy dt

A: We have, y = 4x3 +5x dxdt = 2

Q: 9. (х +у) dx - (у -х) dy %3D0; у (1) %3D1

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Q: 2_dy -y? =2xy dt

A: Given the Differential equation is     x2dydx-y2=2xy.

Q: y(x), find y(4)]. S 4xy' – 4y = 7x, ly(1) = 4.

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Q: Calculate fe Differenthal equationhs ) xy" + Y' = 1 2) YY" = 2 3) Y" - 3y = 0

A: follow next step

Q: 4. y dx -x dy = x + y? .2

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Q: dy y? y(to) = 0 2t dt

A: Given                  dydt=-y22t,     yt0=0

Q: dy = y(1+ y), y(0) = 4 6) dx

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Q: -0.08. Then evaluate dy for a=-3 and dz *+1 %3D Let y = dy = %3D

A: We have to find

Q: | 3yVT – 3y² dy

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Q: dy If = (y – 4) sec? r and y (0) = 5, then y dx

A: Solution: The objective is to find the general solution to the given differential equation

Q: /2 lul = 0.5 / lw*(2) + 2ry(a) – v^(=)] dr. 57 [P(x) + 2ry(x) – y (x)] dx. %3D

A: In this question, given that the extremal J(y)=0.5∫0π/2(y2+2xy-y'2)dx To find the natural boundary…

Q: 2x? dy 2 - y dr dy = cos z dy x + y dr dy 3x O dy E = y (2 – y) ||

A: The given options are  y'=2x2          (1)y'=2-y         (2)y'=cosx       (3)y'=x+y…

Q: Solve the IVP for y(x): dy 3 -y = 18y*, y(1) = 1 da y(x)

A: To solve the question given below.

Q: by (3x? + y²) dx+ (2.xy) dy 7. C: 3D1 from (3,0) to (0,4) %3D - = 1 6.

A: We are given the following integral:∫C(3x2+y2) dx + (2xy) dy over the path C: x29+y216 = 1 from (3,…

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.