-ALef xe Rbe Such thad Xn→x, show that Yn = xi %3D 4 X.

Q: 1) Evaluate the following (general) antiderivatives: a)[9x' +7x+4 dx = b)J9 cos(x)+8sin(x)+7e*…

A: a) ∫9x7+7x+4 dxb) ∫9cos(x)+8sin(x)+7ex+6sec2(x)+4x-31+x2 dx

Q: Find the family of antiderivatives for each ofƒ(x) = ex, g(x) = 4x3, and h(x) = sec2 x.

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Q: Determine the Integrating factor of the DE: y (2³e™y – 3) dæ + x (y+ x*e®v) dy = 0 -3 1

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Q: 2. Given So S√x y² +8 dydx. Reverse the order of integration and evaluate. Draw the

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Q: Find the antiderivative of xe2x/(1+2x)2 from 0 to 1/2

A: Given the integral ∫012xe2x1+2x2dx

Q: Show that y(t) =t-2 ln t is a solution to ty"+5ty' +4y 0. (where t> 0)

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Q: The integrating factor of the DE 2y(x^2 - y + x) dx + (x^2 - 2y) dy = 0 is O x^2 O 2x O e^x O e^(2x)…

A: This question is based on Differential equation.

Q: is given by Oxy = E(XY) HxHy.

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Q: 1- 2xy 7. y = %3D %3D ds e'-2t co dt 9,

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Q: a- If w = x² + 2xy and x, y change from initial values (x = 1, y = 3) By amounts dx = 0.01 and dy =…

A: Given: w=x2+2xy So, dw=2x dx+2y dx+x dy...(1)

Q: --——-^*[e'-In(2t+1)]dt, find g'(x) . dx 4 A e*+ (2x + 1)² 4 B et + (2x + 1)² 2 (C) e*- - (2x + 1)²…

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Q: 2) Obtain the DE with respect to x of (x - h)² = 4(y-k).

A: Sol

Q: Given : S 6x³e**+3 dx. Using integration by parts (S udv = uv – f vdu) and letting u = f(x), dv =…

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Q: kop (e + bx) = (xph + hp x )ch (s

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

Q: If g(x) = - [e' - In(2t+1)]dt, find g''(x) . dx A e* -In(2x+1) 4 B (2x + 1)² 4 C (2x + 1)² 2 D (2x +…

A: To solve the following problem

Q: dy – 5x-2+ 2x-1 – 6; y(1) =7. dx |

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Q: The integrating factor of the non-exact DE: y²dx + (xy – 1)dy = 0

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Q: Express the general solution of dy/dx = 1+ 2xy in terms of the error function erf(4) = dt.

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Q: If x =0.71 and y = 0.67, then value of C in the xsin-(x) V1-x² antiderivative of F(x) = is

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Q: Select the correct antiderivative. dy 1. xp x² + 1 O In(x² + 1) + C 2x (x² + 1)² arctan x + C Inv x…

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Q: Q4 Find dy for all of : dx 3 x(x-2) 1- y = xvInx 2- у 3D x2+1

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Q: IN SA Coefticients 4 Linear in two vanabtes: (x-34+4) dx+2(x-ソ-2)dy

A: In the question it is asked to solve the equation using coefficients linear in two variables:

Q: Find an integrating factor to the linear D. E. In(9 x+16)y+ y =20 9x +16 p(x)= (6 x+ 14) In(18 x…

A: Given the linear D.Eln (9x+16)y'+99x+16y=20we need ti find the integrating factor

Q: dy de =1+eV-z+5 O e*y+5=x+c O ey+5=x+c O y-5x+c O exy-5=x+c

A: given differential equation dydx=1+ey-x+5 find the solution of the differential equation

Q: Q2: Find the general solution of the following linear second order inhomogeneous O.D.E.: ý-y=e*

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Q: 1 z = Vuv, u = 3xy + 2x2 + e"-Y Find zzy at x = 1, y = 1

A: Topic:- function

Q: Find general solution for y"+y=0.5cos(0.8t) and state whether it is undamped, underdamped,…

A: In the given question we have to find the general solution of the given differential equation which…

Q: зхе-МХxcos(Nx) 5- a. Differentiate: y = M csc(Nx)+Nx

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Q: If µ(x, y) = x" y" is an integratingfac. of the the DE. . (1 + 3xy)dx + (xyl + x²)dy = 0 Then, the…

A: A differential equation of the form Mdx+Ndy=0 is said to be an exact differential equation if it…

Q: 5) y ² ( x dy + ydx) = (xy + 2) dyz

A:

Q: If g(x) = - - S^*[e'- In(2t+1)]dt, find g'(x) . dx A ex-In(2x+1) 4 B

A: We can solve this as follows:

Q: 2. Given the joint pdf of X and Y, fxx(x, y) = { '0" (4xy 0<x< y <1 other wise Find the marginal…

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Q: Solve the following DE, using Linear First Order method with initial conditions. y'+2xy x, y(0) = 3

A: Explanation of the answer is as follows

Q: Let y(x) be the solution of the IVP dy - (y - 3)'dx = 0, y(0)=2. Evaluate y(13).

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Q: 2. Solve the IVP 2x + y + 2xyy' = 0, with y(1) = –2. d (Hint: This ODE is neither first order…

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Q: 1. Find the total differential dw. x + y +z 3. w = xyz

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Q: Find the integrating factor of the given Non-Exact DE y (4x + y) dæ – 2 (x² – y) dy = 0

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Q: 1 . Evaluate the integral: S, S (4x³ + 6xy - 3y²) dx dy -1

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Q: Solve the Bernoulli's DE: (x°y3 + 1) dx + x4y2 dy = 0.

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Q: Find the general solution of the following nonlinear first order ariable separable O.D.E.: x?dy +…

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Q: If p(xy) =y is an integratingfactor of the the DE. (12+Sxy)dr + (6xy+ 3x2)dy = 0 Then, the values of…

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Q: ** If g(x) = S [e* - In(2t + 1)]at , find g"(x) dx ex. (2x + 1)2 A ex – In(2x + 1) 4 ex + (2x + 1)2…

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Q: Find the integrating factor: dy 3y = x (1 + x?) dx e3x None of these e-3x x3

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Q: 3t e"dt 2 (1+4e3

A: Let's integrate.

Q: flx, v) = { xe-x(1 + y) x20 and y 2 0 otherwise rmine E(XY). ulate Cov(X, Y) and p. X, Y) =

A: Given Two components of a minicomputer have the following joint pdf for their useful lifetimes X and…

Q: e) f1a* +4)*dt

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Q: Obtain the particular solution satisfying the indicated condition. lnx/e^ydy=xdy ; y(1)=0

A: Follow next step

Domain

In simple mathematics terms, a domain is defined as the space on which all the possible inputs for the function will lie. It can also be expressed as a set of departures for the required function.