Solve the ODE by y Integration a. = 0

Q: d Using the Chain Rule Twice Calculate 1+ Vx2 + 1. dx

A: Given function is 1+x2+1

Q: Q9/ find the integration ſe^( (2x) ^3-1) x2 dx? * 1 а- 6. e2x* -1+c 1 b- e2x3 +C 1 .2x3–1+

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Q: Using the method of successive approximation, solve the integral equation, y(x) = ex + y(t) dt.

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Q: Rewrite the integration in terms of u. 2x dx = du x² + 16

A: Given :∫032xx2+16dx

Q: Solve the two items using Integration by parts. 1. (x' V9-x? dx

A: Question - 1:- Given: ∫x39-x2dx Formulas used: ddxxn=nxn-1ddxconstant=0ddxfgx=f'gx·g'x        Chain…

Q: Reverse the order of integration in S S(2xy + 1)dxdy and then evaluate.

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Q: (10xy + 8y - 32y +7)dx+ 2(x +2xy– 4x)dy =

A: To solve the differential equation , I have used the method of exact differential equation and then…

Q: Solve the integral. dx 9. J Ta – x)(b – x)

A: The given integral is, ∫dxa-xb-x To solve the given integral, we use the partial fraction,…

Q: The integration of ſ, Vx tan-'Vx dx is

A: Given that  The integral is

Q: t2 +t dt 2

A: ∫t2+t2 dt

Q: 3. Solve this third-order ODE by using the method of undetermined co- efficients: y" – y = exp x . -…

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Q: Q1) use two method of numerical integration to approximate x?cos(x?) dx n = 8

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Q: Solve J. e-t sint dt. 0,

A: Introduction: The Laplace transformation is very useful in determining the integral. The Laplace…

Q: Jay ti dx dy Compute the integration

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Q: Solve the separable equation using the integral factor  y⁴ y¹ +y¹ + x² + 1 = 0

A: Given equation is y4y'+y'+x2+1=0solve it

Q: Solve the differentfial equation by Using the method of integrating factor for e= dy 24. 2%. dz e-x

A:

Q: Solve the integral. sec? x etan x dx 3. y1+etanx

A: Given the integral ∫sec2x etanx1+etanxdxWe need to find the integral.

Q: (t² + 2t) dx = 2x + 8, x(1) = 1 dt

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Q: Find the integration Sx cos 2x dx

A: Here we have to use integration by parts to find the answer.

Q: Q2: Find the integration by applying substitution method: 7 dX (X - 1)VX- 2x - 48

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Q: Solve the integral equation F(x) cos px dx =. [1-p,0sp 1.

A: Since you have asked multiple questions, we will answer the first question. If you need answer for…

Q: Solve the ODE: dy (x' +4x) 0 using separable variable method: dx x(sin 2y +4)

A: The differential equation is as follows : dydx-(x5+4x)x(sin2y+4) = 0 Hence we get dydx =…

Q: Q1) use two method of numerical integration to approximate |x*cos(x?) dx n = 8

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Q: Solve the general solution using the integrating factors by inspection (x³y³+1)dx+x⁴y²dy=0

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Q: e dx (1) S. 1-e2x (integration by substiution)

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Q: 2. t23* dt

A: The given problem is solved below in detail.

Q: Solve the integral: dy dx. x2 H/4

A: To solve: The integral ∫141∫x2xxydydx. Formula used: ∫xndx=xn+1n+1+C Here, C is constant of…

Q: sin x e" dx Cos x

A: To evaluate the given integral.

Q: dx : A) Find the integration:

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Q: c) Calculate the integration Y+1 dydx

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Q: Q₂) Compute Z² dz along the straight line from (0) to (4 + 4i), then verify your result by using…

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Q: Solve the separable equation using the integral factor  Sinx dx + ydy = 0, when x=0, y=1

A: Topic:- application of integration

Q: Solve the initial-value pxoblem dy dr COSX-Sinx t %3D yro)%3D0 Using Adams. Moulton.

A: Given differential equation is dydx=cosx-sinx+y Let  f(x,y)=cosx-sinx+y                 (1) 0≤x≤0.5,…

Q: - Solve the linear ODE using an Integrating Factor. x². dy dx + 2xy = 3sin(8x)

A: solution is given below

Q: The

A: This is Linear Differential equation in x. We use method of separation of variables.

Q: dx 3x2. dy ' y + 1 7(у + 1) 3 о

A: Let's find.

Q: Q5; Use three iteration of Picard's method to solve dy = 3x+ y when x=0.1, given that y 1 dx for…

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Q: Q#2: Find the Numerical Integration of Jo xe2*dx with 1 step size.

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Q: Solve the ODE by integration or by remembering a differentiation formula. 1. y' + 2 sin nx = 0 2.…

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Q: Solve the integral equation f(x) cos Ax dx = e. %3D

A: Given integral is, ∫0∞fxcosλxdx=e-λ The right-hand side is a Fourier cosine transformation function…

Q: In each part, confirm that the formula is correct, and state a corresponding integration formula.…

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Q: Q2: Find the double integration ff (4x + 2)dydx D={(x,y):0<x<2,xẻ<y<2x}

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Q: Solve the integral equation F(x) cos px dx: [1-p, 0sps1 0, p > 1.

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Q: Find an integrating factor. (6x3y + 2xy + 2y³) + (x2 + y?)y' = 0 µ(x) : Solve the giv en equuation

A: Concept : First we have to check given equation is an exact differential equation or not. If…

Q: 2) I = S t? sin ßt dt

A: Standard Formula that has been used are ∫sin(ax)dx=-cos(ax)a∫cos(ax)dx=sin(ax)a

Q: The integration A. 114 Β. π C. 0 D. 1/2 Z|7 sinc(4nt) dt has the value (hint:use the FT)

A: Given integral is ∫−∞∞sinc4πtdt. We have to evaluate the given integral. Here, ft=sinc4πt. Now, for…

Q: Solve for the differential of y when y= sinxx, x=-, and dx=-. 3 2 A B D

A: In this question we have to solve the differential of y.

Q: Q4/ A/ Find the integration for the following functions (chose three) 1- sa (3x³+3x-5x²) dx 2 - S 2x…

A: