The characteristic equation for a 5th​ degree, homogeneous, constant coefficient DE is​ p(x)=x^3(x^2+1). Which linearly independent functions will be used to form the general​ solution?   A. ​1,x,x^2,cos(x),sin(x)   B. ​1,e^{-x},xe^{-x}, cos(x),sin(x)   C. ​x,x^2,x^3,cos(x),sin(x)   D. ​1,e^x,xe^x, cos(x),sin(x)

Q: Using [ y = e^(2x) (c1 + c2) + 3/2x2 (2x) ] and [ y = ( c1 + c2x ) e^(2x) + 3x/25 sinx + 4x/25 cnx +…

A: The given differential equation is;  y'' - 4y' + 4y = 3e2x + xsinx

Q: Solve for a) given y= 2f(x) solve for x b) given y=-3f(2x) solve for x c) given y= f^-1 (4x) solve…

A: Given Functions are as follows

Q: 7. y = cos`x sin'x %3D 3 A. – 4 cos x sin x B. – 2 sin sin 2x 3 2 C.- 4 cos´x + sin' D.- 2 sinx cos…

A:

Q: Find f'exo if fex)= Find f'ex) if fcx)= (5x² + 1) cos(2x) 100 sec² (2x + 5) (x + 2)¹ 3

A: fx=5x2+1cos2x3sec22x+5x+2100

Q: The solution of the following Bernoulli's equation y' + 3x²y = 4x²y² is: Oy= 3/(4+3Ce^(x^3 ) ) Oy=…

A: The given Bernoulli's equation is, y'+3x2y=4x2y2. To find: The solution of the given differential…

Q: The general solution for the equation y'=x*e(x^2+y) can be given in the form of: ?ex^2+2e-y=k a) x…

A: Solve by separable variable method

Q: what terms from the equation make the equation nonlinear? and why X" + x + (x)² + x + x³ + sin(t) +…

A:

Q: Get the first order derivative of the function x + sin(y – 2x) - 1= 0 - 2 1 a. y' = cos(y-2x) 1 b.…

A:

Q: The solution of the IVP, y' = -2xy, y(0) = 2, is: %3D

A:

Q: Differentiate. G(x) = (8x² + 9) (4x + Vx) Gʻ(x) =D %3D

A: We know that, from product rule of differentiation ddxfx·gx=fx·g'x+gx·f'x                  ⋯⋯1 We…

Q: Which of the following is the general solution to the equation (5x 4y 4 +4e 4x-9y -2xy)dx+(4x $y…

A:

Q: Obtain the general solution using variation of parameters (D²+3D+2)y=cos(e^-x)

A: We have to solve the given differential equation by variation of parame

Q: Consider the estimated quadratic model   y ^ = 23 + 1.6x − 0.02x2. Now, Predict y when x equals 10,…

A: The objective is to find Predict y when x equals 10, 20, and 30.

Q: Find the solution. (403+12D²+13D+10)y = 0. @ y=c,e+e>(c,cosx + c sinx) +c,sinx) -3x y =…

A:

Q: Evaluate e^(z^2) if z = x+yi Select the correct response: e^(x^2+y^2) [(cos 2xy) - i sin 2xy)] none…

A:

Q: ) = 3x + sin x - e^x solve using bisection method of non linear equations of one variable

A:

Q: Which of the following is the general solution to the equation (2x+9)y" +(2x+7)y-2Y3D0? O a. y=c_1…

A:

Q: 1) y" + 4y = 4 sec (2x) 2) y" + y = csc(x)

A:

Q: Solve the equation (2х + 6) (2y? + 3) dx + 4y(x? + 3x + 2) dy %3D 0

A:

Q: 5. (y" – y) = e-X cos(3x) %3D

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

Q: guess the form of the solutions 1- y’’ - 2y’ -3y = 3sin(5t)+tcos(5t)+2te^-t 2- y’’+2y+10y=4te^-t-…

A:

Q: Find f. F"(8) = sin(8) + cos(8), f(0) = 5, = 5, f'(0) f'(0) = 3

A:

Q: Solve the equation [cos (2y) - (3x^2)(y^2)]dx +[cos (2y) - 2x sin 2y - (2x^3)(y)]dy = 0

A: To solve the given differential equation. First we check whether the differential equation is exact…

Q: A cable hangs between two poles of equal height and 30 feet apart. Set up a coordinate system where…

A: We have to find the length of the curve   for