Solve the equation. f' (x) = 6f (x) & ƒ (2) = 9. f (x) = e6x+9 O f (x) = 9e6x– 12 O f (x) = 9e²a+6 O f (x) = 6eæ+2

Q: 2. Solve the initial value problem, D²ƒ – Dƒ = 0 f (0) = Df(0) = 1 with

A: Given  D2f-Df=0 with f(0)=Df(0)=1 The auxiliary equation is  m2-m=0 m(m-1)=0 m=0 or m-1=0 m=0, m=1…

Q: Q2. Solve the initial value problem 2- y = f(x) with initial condition y(0) = 2 and dx (0, 0<x<1…

A: Given differential equation is. dydx-y=fx                                      ........1 The given…

Q: 3. General solution of (ylny - e-xy)dx + ( + xlny) dy = = 0

A:

Q: For each case, find a differential equation whose general solution is:   y = c1e2t + c2e-3t    y…

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Q: Solve the Initial value problem x' -x=8(t-2),x(0) =x' (0) =0

A: We use the Laplace transform to solve the given initial value problem.

Q: Which of the following is true in solving the initial value problem=x³—4—3e³¹,y=1whenx=0 ? A --4x-e³…

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Q: f'(x) = cos x; y (G) = 3 %3D

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Q: 4 solve the D.E " -X² Joly =0 3x2 ydx + LY

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Q: Solve the initial value problem by finding the particular solution бу + у 3 6 сosh x, у(0) — 0.2,…

A: The given differential equation is  8y''-6y'+y=6 cosh x  , y(0)=0.2, y'(0)=0.05 Firstly finding the…

Q: Find the general solution of the DE y’’ = xsin(x)

A: Topic = Differential equation

Q: Q2: Use two iterations of N-R method to solve the nonlinear equation with estimated solution xo = 2.…

A: We have to use the two iterations of the Newton-Raphson method to solve the nonlinear equation with…

Q: (a) Solve the initial value problem X'(t) : -2 1 X(t), X(0) = (Ь) Describe the behavior of the…

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Q: Find the particular solution that satisfies the differential equation and the initial condition. x²…

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Q: Solve the DE: (xy'+y)(1+2e* +e*)- xe* = 0

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Q: 5. Solve y"-y'-2y = e-x+1, y(0) = 0, y' (0) = 0 by undetermined coefficients.

A: Consider the given differential equation and initial conditions

Q: Find the solution of the equation yy' = x ex-y with initial condition y (0) = 0. Is it possible that…

A: A differential equation is an equation that involves derivatives or differential coefficients or…

Q: 12. Test the equation for exactness and solve for the general solution. (2x - 3y) dx + (2y 3x) dy 0.

A:

Q: Find the function f(x) by solving the initial value problem. f'(x) = ex - 2x ;   f(0) = 2

A: Given : f'x = ex-2xf0 = 2

Q: Solve the initial value problem. y dy dx = 9x ex, X The solution is y(x) = 9x ex - 5x. y(1)=9e-5

A:

Q: 4. Solve the initial value problem- dx dy 3x? +4x + 2 2(у-1) y(0) = 2 and state the interval in…

A: Given differential equation is : dydx=3x2+4x+22y-1 To solve the given differential equation.

Q: Solve the given initial-value problem. (Use x as the independent variable.) 2y'y" = 1, y(0) = 2,…

A: Here we have to solve the given initial-value problem.    2y'y"=1 , y(0)=2 , y'(0)=1

Q: Choose the solution value of x'' + w2x = fsinwt with initial conditions x(0) = 0 and x'(0) = 0

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Q: Find the particular solution that satisfies the differential equation F'(X) = 10x − 12x3 with an…

A: Given the differential equation: F'x=10x-12x3 Initial condition: f3=2

Q: Use variation of parameters to solve the initial value problem, given the solutions y1, y2 of the…

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Q: Find the solution of the D.E whose solution is given as y = 2(x² – 1) + Ce-x2.

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Q: Find f ( x) by solving the initial value problem. f'(x)=e^(x)-4x;f(0)=3

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Q: Solve the initial-value problem for y as a function of x. (16 – 2²) dy 1, y(0) = 7 dæ Y =

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Q: Q2/ Solve the differential equation by using the appropriate method y' = (x + y - 5)2 %3D

A: The solution of an ordinary differential in the form of can be found by the technique of separation…

Q: solving

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Q: dу ху+2у- х-2 dx xy- 3y+ x-3

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Q: Part II Solve the initial value problem. b. 3y(x?- 1) dx+ ( x³+ 8y– 3x) dy=0 y (0) = 1

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Q: xy' + y = e", y(1) = 2 %3D

A:

Q: Solve the given initial-value problem. x-( -(:) x-() X' = = X + %3D

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Q: 4. Solve the IVP y' = 2x-3y +e¯* y'= 2x- 3 y +e * with y(0) = 1 y(0)= 1

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Q: x² – y? with y(2) = 4. XY %3D

A: Solve the differential equation y'=x2-y2xy with initial condition is y2=4. Solution: A first order…

Q: Find the value of y (0.4) if y' + 0.2y = 0, y(0) = 5. Solve analytically.

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Q: Show that y = x (1 – e*-1) is a solution | to y" – y' + e"-1 = -1

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Q: Solve the given initial-value problem. (Use x as the independent variable.) 2y'y" = 1, y(0) = 8,…

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Q: Find the particular solution of the differential equation that satisfies the initial condition(s)…

A: topic - differential equation

Q: For the given initial value problem, identify all the points (x0, y0) where the given equation has a…

A: We will use properties and continuity of functions to identify the points for our problem.

Q: Q4: Solve the differential equation: 8- dx2 d²y 69 + y = 6. coshx dy dx

A: Some formulas: coshx=ex+e-x2 Given differential equation is: 8y''-6y'+y=6 coshx Auxiliary equation…

Q: A- solve = x + y² with condition y (0) = 1, x o= 0 to x =0.2 and h = 0. by Rung kutta dx method 4th

A: The given differential equation is dydx=x+y2 with conditions y0=1, x0=0 to x=0.2 and h=0.1.

Q: Solve the initial value problem f'(x) = vx +,f(1) = 2.

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Q: Solve the separable equation (initial value problem) dr+rtanφdφ =0,r(π)=0

A: Given equation - dr+rtanϕdϕ = 0dr = -rtanϕdϕdrdϕ = -rtanϕdϕdrr = -tanϕdϕIntegrating on both sides -…

Q: Solve the initial-value problem. dy dx3 . for x20 with y(0) =3 The solution to the initial-value…

A: To find: The solution of initial value problem. Given: The differential equation is dydx=x33 for x≥0…

Q: Solve the given initial-value problem. x - (; -1 -2 3 4 x +(:), xco)- - ( ) X' = 6 X(t) :

A:

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.