x?dx 1. S: V2x-x²

Q: ydx + (2x +3y)dy = 0 %3D

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Q: C = dx (1- x²)) X tanh-1 %3D

A: As per the guidelines, we are supposed to answer only one question at once. Kindly repost the other…

Q: Terential equation. (x + 6y²) dy = 0 (2x³ + y) dx – xdy = 0 ydx – %3D

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Q: (xy² + y-x) dx + x(xy+1) dy = 0

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Q: 16- x, y) dy dx = (x, v) 16 - y

A: We will change the order of integration.

Q: Q! Salve! y? -y?+2y=Sin3× using D-opevtor Method

A: The given differential equation is: y'''-y''+2y=sin(3x)

Q: x? -dx ² 2 Integrate by trigonometric substitution: V7 -x

A: We have to find the integral

Q: VI-x? x dy dx •1/2 9. V3x

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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: 2 dy y4/y²-25

A: use the trigonometric functions as required.

Q: dx 1十X5

A: We will solve the question using trapezoidal formula- I=h2y0+yn+y1+y2+y3+......yn where h = step…

Q: u - 1 Find dy/dx, given y : and u =Vx + 2. u* + 1

A: We can find the derivative as below.

Q: inteeral equation : [) dx - 1 +t+?. Y (x) = 1+t+?. Solve the V(t – x) Using L.T and convolution

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Q: P/ by method of variation of Parameters -X find ゾーン Y-Y = e Sine

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Q: 4 – 9x?dx using integration by parts and trigonometric substitution.

A: To evaluate the integral: ∫4-9x2dx Solution: Let substitute x=23sint. Differentiating both sides,…

Q: Trigonometric Substitution SV9-y dy Vy dx 6. S e 2x+1

A: Due to Bartleby guidelines, only 1question can be solved. Please repost the remaining questions to…

Q: y = csc (x’ + 10x), Find dy/dx O (7x6 + 10) csc (x7 + 10x) cot (x7 + 10x)

A: Given: y=cscx7+10x

Q: Find I using integration or geometry: I = 5 dx dy .

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: The domain (Dx) of y = 1 Vx-1

A: We have given ,         y = 1x-1 As y is under the square root its means y ≥0 .

Q: SiSi dx dy dz Q4) Evaluate xyz

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Q: Non-Exact H.W: (2xy ey+2xy³+y)dx + (x²yey-x³y²-3x)dy=0

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Q: Diffential Equation by Substitution:   DE (x+2y-1)^2 dx = dy

A: We have to solve differential equation.

Q: Mesin(2x) dx = eSin(2x) + C, then the M is equal to B %3D

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Q: dy = 2y-2 find the solution of dx

A: dydx=2y-22-ydy=dx4 Integrating w.r.t. both sides- ∫2-ydy=∫dx4∫2-ydy=x4

Q: exact diffential equation of (y+2xy³)dx+(1+3x²y²+x)dy=0

A: We have to solve the exact differential equation: y+2xy3dx+1+3x2y2+xdy=0 Rewriting the equation, we…

Q: 4x -dx using Trapezoidal Rule with n=5 x2 + 4 Evaluate

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Q: linear first order equation y dx = (e + 2xy – 2x) dy %3D

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Q: x2 2. S dx 4-x2

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Q: dy -. Find using any method. Express your answer in dx Let y = 67cos -e" %3D terms of x only. dy %3D…

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Q: Bifferentiate the following function. 3x +7-5e* y= dy dx

A: given :

Q: cof z-csc z dx So 2cotzcosz

A: a detailed solution is given below

Q: Integrate by substitution. Check your answer by differentiation. dy |y+8

A: Here we have to integrate the given integral.

Q: 4- fil0,00)→R all continious Aunction aro Sx³f(x?)dx= Sx f(x) dx %3D show this.

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Q: P/ by method of variation of Parameters -X Find Y-Y = e sine دیگا

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Q: By using appropiate substitution, solve dy hpT i. x2 dx 1 = xy – y² ii. – 2. (2х + у)е2»+у | dx

A: Consider the provided question, (b) (i)

Q: 1 -dx a² (x–1) The solutiom indetail -

A: We can find the integration as below

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

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Q: classify and find general salutin of di ffeten tind equation :- (l-2x² tany) dx - (x³sec_y ) dy=o '

A: This is a first-order differential equation. We will assume some variable for tany and can solve…

Q: dy when x = -3 and dt dx Given y= 4x +5x, find = 5. dt dy (Simplify your answer.) dt I3I II

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Q: dx Find -given that dt 7x² + 6y² = 13 x = 1, y = - 1, and Give your answer as a simple fraction. dx…

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Q: x+1 Find S dx. [Hint: Rules of integration and Trigonometry substitution] 9+x²

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Q: dy = a-x dx when x 1, y = 2 when x = 2, y = 0 %3D what is the value of a?

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Q: (с) (2x3 + у) dx — x dy %3D0..... [EXACT DE]

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Q: reflection across the x-axis M Ay D

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Q: dy at x= -2. 1 If y =-,, find xp dy at x= dx - 2 is 1 The value of . (Simplify your answer.)

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Q: x dy-y dx = x3 dx y" Answer: 4x + x4y + x¹y = Cy.

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Q: dx 4. S x²Vx2-9

A: 4). Given: I=∫dxx2x2-9   ....(1)   As we know from the trigonometric identities; 1). cosx=1secx 2).…