Find the value of the constant C for which the integral 3 3C dx x + 25 X + 5 converges. C =

Q: Q3) Solve the following boundary value problem using finite difference method dy +2y = 0 dx y(3)=…

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Q: The solution of dy/dx = y with initial value y (0) = 1 bounded in the interval (a) - 0 1

A: Bounded solution in the interval

Q: solve the given initial-value problem up to the evaluation of a convolution integral. Q. y′−ay=…

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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: Solve the initial value problem. dv + sect, v(0) = 4 %3D dt 1+?

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Q: Solve the initial-value problem for x as a function of t. da (t - 10t + 21) = 1, (t > 7, z(8) = 0)…

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Q: The integral of the given function ſ 3(x-1) dx is equal to (3x+1)ž

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Q: 17. Find the values of p for which the integral So dx converges. OpE (-1,1) Op21 Op 1 Opsl

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Q: 2. Consider the functions: f(t)=√1+t² and g(t) = 2t Find the convolution of the two functions by…

A: We have to find convulation of given function.

Q: (2a+1) 5. S -dx (z+2)*(x–1)*

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Q: 3. S "(o2-1)dv v2+1

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

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Q: 1- xy = y+ x² sin x , y(n) = 0

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Q: Solve the initial value problem and figure out its interval of validity dy 3y = x¹e² with y(1) = 0.…

A: Given: The differential equation is xdydx-3y=x4ex. The given initial condition is y1=0. To solve:…

Q: Solve the initial-value problem for x as a function of t. dx (2t3 – 2t? + t – 1) 12, г (2) — 0

A: Given,

Q: Drove that 3 e dx converges to 9 3e

A: Explanation and solutions is given below.....

Q: Solve the following differantial equation using finite difference method. d²x(1) + x(t) = 0 dt? dx…

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Q: The integral 2a12 + 5x° is equal to -dx 3 x5 + x3 +1 (a) -25 + C (2) +2² + 1)* (b) z10 +C (1 + کے +…

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Q: 2. Find the interval [a, b] for which the value of the integral (2 + x − x²) dx is a maximum.

A: ∫ab(2 + x -x2 )dx here for get maximum value we have to differentiate the function  so here first…

Q: (t² + 2t) dx = 2x + 8, x(1) = 1 dt

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Q: Q3) Solve the following boundary value problem using finite difference method d²y dy given that 3- +…

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Q: Solve the following differantial equation using finite difference method. d²x(t) + di? dx x(1) = 0…

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Q: Q5:al Using the Runge-Kutta method, solve x = 0.2 when h = 0.2. dy = x + y² with the initial…

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

Q: Find the integral |(2 + 1)e* dz. (z + 1)e²² dz +C

A: solution is given below integration by parts...

Q: 2 4 Q3) Evaluate the integral || xe" dy dx 0 x?

A: LetI=∫02∫x24xey2dydxchange the orderI=∫04∫0yxey2dxdyLet∫0yxey2dx=x∫0yey2dx∫0yxey2dx=ey2[x22]0y…

Q: 2. Reverse the order of integration and then evaluate. o S x² sin(xy)dxdy a.

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Q: Express the solution of the following initial value problem in terms of an integral. dy 6+x У (6) %3…

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Q: Solve the Indefinite Integral. xe²t S dx (2x+1)² A [1-21] +0 e2x 2x C 4 2x+1 B. 2-2(22+1) + C 4 C.…

A: SOLUTION-

Q: (x²y)dx + (x³ + 2y³)dy = 0 ||

A: According to the given information, it is required to solve the differential equation using…

Q: 8. Find the value of the constant C for which the integral 11x 11C dx x* + 1 4x + 1 converges. C =…

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Q: 2. Given the integral: S, e'/x dx; n = 8

A: Given,          ∫13e1/xdx;  n=8

Q: Use a comparison to determine whether the integral 15/2 J4.3 x dx converges or diverges. - 18 1 dx,…

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Q: The correct value of dx is equal to 3-x O A. Since the integral converges to 2/3, none of the given…

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Q: Given: S^(1+ 2x)e-* dx. Using integration by parts and letting u = -1- 2x, dv =¿f(x)dx, then the…

A: we have to evaluate, ∫0∞1+2xe-xdx Let u=-1-2x and dv=32-23e-x where fx=-23e-x…

Q: Solve the following using Integrating Factor by Formulas. a.) 2y(x2 - y + x)dx + (x2 - 2y)dy…

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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: The

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

Q: dx S. 2x - 1 e

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Q: Solve the initial-value problem for x as a function of t . (2t³ − 2t² + t − 1) 12, x(2) = 0 dx dt =

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Q: -8 dx c – 2)(x² + 4) an upper-case "C" for the constant of integration.

A: We use partial fraction to find integral

Q: 2. S*3*+2 dx x+2

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Q: Find the general solution of the ODE. d'y dy +3. dx² dx Stre

A: Given d2ydx2+3dydx=5x+xex

Q: Find any value of c for which the improper integral cx + 36 x2 + 1 9. da x (4 x + 5) converges.

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Q: Trapezoidal (Use n = 9) 3 5. S¹ (5√x-³) dx √x 6. √² (5ex - e)dx

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Q: Q4: Solve the following integrals:- 4dx dx (1) S: (2) S sec xesin x (3) S x sec² x dx dx (4) J 2+3x…

A: Using definite integral

Q: e ( + 4)2 dx = Evaluate the integral if it converges. Enter the exact answer, or enter na if it…

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Q: Solve the following initial value problem for  y = f (x). dy dx  =  e−3x, y = 79  when  x =…

A: dydx=e-3x and y=79 whrn x=0

Q: Q2) Solve the following problem over the interval from x = 0 to 1 using a step size of 0.25 where…

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Q: Q2)For what value(s) of k does the integral converge : -o kx 1 x²+1 dx 2x Then evaluate the…

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Q: dx is equal to The correct value of A. 2 B. Since the integral converges to 23, none of the given…

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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.