Given that y, = sin(2 x) and y2 = cos(2 x) are solutions to y" +p(x) y' + qx) y =0. Let y, = V1 Y,+v2+y2 be the particular solution to y" +p(x) y' + q(x) y =6 x that obtained by the variation of parameters method. Find v,(x). vXx% sin(2 x) +x cos(2 x) a b. v,X)= 1x sin(2 x)+ cos(2 x) C. none d vo)= x sint2 x) + cos(ex) e v,X)= x sin(2 x)+ cos(2 x)

Q: Solve the following initial value problem using the undetermined coefficients method: d'y dt2 + y =…

A: Given d2ydx2+y=8cos2x-4sinx with yπ2=-1,  y1π2=0

Q: What is the solution to the initial value problem y" – 2y' + 10y = 0, y(0) = 3, y'(0) = 0 ? A) y =…

A: To find The solution to the given initial value problem .

Q: Find the solution of the differential equa­tion that satisfies the given boundary condition(s) . y'…

A:

Q: The boundary-value problem y =y+2y + cos x, 0<xs, y(0) = -0.3, y y() =-0.1 (sin x+3 cosx). Use the…

A:

Q: Solve the initial value problem. dy = 12 sin 2 x dx x cos x, y(0) = 3. HINT: First integrate the…

A:

Q: 3) Find the solution of Initial Value Problem dy 2x-sin y dx 2x cos y ; y(4)=0

A:

Q: Find the solution of the given initial value problem in explicit form. 75 ㅠ sin (2x) dx + cos(7y) dy…

A:

Q: Give the form of a particular solution of -4x yl4) – 256 y =2 e**+3 e+ cos(4 x) – 2 a) O z=Ae -4х +…

A: OPTION D IS CORRECT.

Q: 1. Find the solution of the PDE with the prescribed auxiliary conditions by the method of separation…

A: The given problem is to find the solution for the given wave equation partial differential equation…

Q: Solve the initial-value problem (2y sin x cos x + y sin x)dx + (sin'x-2y cos x)dy 0 by using…

A:

Q: 2. The boundary-value problem y" = y +2y+ cos x, 0sxs y(0) = -0.3, y() =-0.1 has the solution y(x) =…

A:

Q: Given that x(t) = c¡ cos wt + cz sin wt is the general solution of x" + w²x = 0 on the interval (-*,…

A: 10 Given solution of differential equation is x(t)=c1cos ωt+c2 sinωt of the differential equation…

Q: Solve the differential equation t dy dt 1 y(0)=1 by the Euler method with h=0.1 to get y(0.2). Then…

A: Hint:  The recurrence formula in Euler's method is, yn+1=yn+hfxn,yn, where h is the step length. The…

Q: . Find the general solution to y + 2x = 5y³. dy . Solve the initial value problem of (sin x) = y cos…

A: Topic:- differential equations Note :- as per our guideline if more than one question uploaded than…

Q: Verify that y=2 cos(3x) is a solution to the initial value problem: y"+9y=0, y(0)= 2

A:

Q: Find the particular solution of (cos x x sin x + y2) dx + 2xy dy = 0 that satisfies the initial…

A: Please see the explanation below

Q: Solve the initial-value problem: dy cos x - sin x + y, 0<x< 0.5, y(0) = 0 dx using a) Fourth-order…

A: Given function is                                                   dydx=cosx-sinx+y, 0≤x≤0.5 with…

Q: Determine (without solving the problem) an interval in which the solution of the given initial value…

A:

Q: Determine the solution of the simultaneous nonlinear equations and compute the errors. sin(xy) – x²…

A: Hughhjfkgnmghgvnhvjhjgfghghfhg…

Q: Solve the initial-value problem: dy cos x – sin x + y, 0 < x < 0.5, y(0) = 0 dx using a)…

A:

Q: 1- Solve dx = cos x + y, where y = 2.0 at x 0 take step size h = 4x = 0.1 and solve for 0 ≤ x ≤ 0.2…

A: Given : dydx=cos x+y where y=0.2 at x0 takes step size h=∆x=0.1 To find: Solve for 0≤x≤0.2 using…

Q: Find the solution of the given initial value problem in explicit form. π sin(2x) dx + cos(9y) dy =…

A: Given: Now,                sin(2x)dx+cos(9y)dy=0Integrating both sides we…

Q: 1. Find the general solution (5x*y – sin (x))dx +(2x°y-cos (y))dy = 0

A:

Q: find the integrating factor of the given linear DE and general solution of the y'+1/x (y)=cos(x)

A: Consider the given linear differential equation. y'+1xy=cosx The objective of the problem is to find…

Q: 4. Obtain the particular solution of (D² + 4) y = sin x + sin 2x

A:

Q: (b) Find the solution for cos(x) − (1 + x²) x − 2xy = - - with the conditions y(1) = -1, y(2) = 2…

A: Note:-  For this problem if you want general solution for this problem then please resubmit problem…

Q: Solve the initial value problem: cos z – 3x?y – 2æ) dx + (2y sin x – x° + In y) dy = 0; y (0) - -- -…

A:

Q: A rectangular plate with insulated surface is 10 cm. wide and so long compared to its width that it…

A: The two-dimensional heat equation is given by The steady-state heat equation without a heat source…

Q: Solve the initial value problem y" – y = cos(x) with y(0) = 0 and y (0) = 1.

A: Given differential equation is y'' - y = cos(x) with y(0) = 0  and  y'(0) = 1

Q: Find the solution to the initial value problem y (z) – 6 ( y (x) ) + 10 y (x) =-2 sin (3 z) + 36 cos…

A:

Q: Solve the initial value problem dxdt+3x=cos(2t)dxdt+3x=cos⁡(2t) with x(0)=−1x(0)=−1. x(t)=

A:

Q: Find the general solution of the equation x²y" + xy' + y = sec(ln x), given that yi = cos(In x) and…

A:

Q: Find the solution of the given initial value problem in explicit form. π ㅠ sin (2x) dx + cos(7y) dy…

A:

Q: Find the solution of the given initial value problem in explicit form. sin(2x) dx + cos(8y) dy = 0,…

A:

Q: 2. Find the particular solution of Vx2 + y2 )dx – x dy = 0 ; y = 1 when x V3. -

A: Given differential equations homogeneous differential equation of first order we will do the…

Q: (b) Find the solution for cos(x)- (1+x²) – 2xy = z with the conditions d²y dx2 1+x2 y(1) = -1, y(2)…

A: According to Expert guidelines, I can solve only first question

Q: Find the solution of the given initial value problem in explicit form. 75 π sin (2x) dx + cos (7y)…

A: The given initial value problem is                        sin2xdx+cos7ydy=0,  yπ2=π7 We have to find…

Q: Use the method of integrating factors to solve the given initial value problem.…

A: The given equation is

Q: 4. Solve the heat equation du +et sin(3.x) with the boundary conditions u(0, t) = 0, and u(7, t) = 1…

A:

Q: Find the general solution of the nonhomogeneous equation y " - 3 y "+4 y ' – 12y =e + 2 1 3* + C,…

A:

Q: Using the variation of parameters method to find a particular solution of a nonhomogeneous DE with 3…

A:

Q: Solve the initial value problem dx/dt+2x=cos(3t) with x(0)=−1.

A: This is a first order linear Ordinary Differential Equation of the form x't+ptx=qt Integrating…

Q: Find an explicit solution of the given initial-value problem. √₁ - y² dx - √1 - x² dy = 0, y(0) =…

A:

Q: Find the solution of the given initial value problem in explicit form. ㅠ sin (2x) dx + cos(7y) dy =…

A: Here we use basic integral to find the solution.

Q: Determine the solution of the simultaneous nonlinear equations and compute the errors. sin(xy) – x²…

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

Q: Find the general solution of (x + y) cos ydr + (a cos y - sin y)dy = 0. |3|

A: Differential Equation: A differential equation is an equation that contains one or more terms and…

Q: Determine the solution of an initial value problem; 2e cos2x dx + (e'sin2x+3y sec?y2) dy=0 y =0…

A:

Q: Solve the initial value problem: y' = -2xy, y(0) = 1 Use Euler's method with h = 0.2 to obtain an…

A: Given differential equation is                                                y'=-2xy2,   y(0)=1,…

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.