determine the nature of the critical point and draw the phase plane of x'=Ax d) e) (-2-3) 3-4 1 -1

Q: 3. t(t-4)y" + 3ty' + 4y = 2, y(3) = 0, y'(3) = -1

A:

Q: Consider the following (x²-3x+1)y" -(x²-x-2)y'+(2x-3)y=0 on the interval I = (3,00) Verify that Y₁…

A:

Q: What is the integrating factor of the equation (2xy*ev + 2xy³ + y)dx + (x²y+ev – x²y² – 3x)dy = 0 A…

A: We have to choose the correct answer from the given option according to the given condition

Q: t²y' + 2ty - y³ = 0

A:

Q: b) Determine the characteristic equation for y" + 3y + 2y = 0. c) Find the general solution for y" +…

A: The differential equation is:To Do:Determine the characteristic equation and solution to the given…

Q: Q5. Use the method of undetermined coefficients to solve (a) y" + 2y + y = x²e-". (b) у" — 2у + 5у 3…

A:

Q: If y, and y₂ are linearly independent solutions of t^2y" + 5y' +(2+t)y = 0 and if W(y₁, y₂)(1) = 3,…

A: Given differential equation is t2y''+5y'+(t+2)y=0   Also, given y1, y2 are Linearly Independent…

Q: Is the function y = Cx? a solution to the ODE y" – xy' + y = 0?

A: Using Derivatives.

Q: Obtain two linearly independent solutions valid near x = 0  xy" + x(x - 1)y' + (1 - x)y = 0

A:

Q: The orthogonal trajectories of the family of curves y = cx² is (A) 2x +y2=k (B) x²+2y² = k © x=ky² D…

A:

Q: show that the solution y(t)=e^2t(cos(t)-2sin(t)) is linearly independant.

A:

Q: Eliminate the constant: 3r y=c₁₂e²²+c₁₂e² Oy"+y'-6y=0 Oy"+ 5y¹+6y=0 Oy"-5y¹+6y=0 Oy"-y'-6y=0

A:

Q: Obtain the particular solution 1. (D³ +6D² + 12D + 8)y=0 when x = 0, y = 1, y'= -2, y" = 2 2. y" +…

A:

Q: y" + 4y' = 3sin2t + tcos2t %3D

A: The solution for the above question is as shown below.

Q: 3) Consider the IVP y' = x − 2y, y(0) = 1/2. Determine which of the two curves shown in the figure…

A: The solution of the differential equation is defined as the function that satisfies the equation.…

Q: - choose the correct answer If y = t^2/(t^2+1) and t= v(2x+1) the = dyldx %3D 1/N(2x+1) O 2(x+1)^2 O…

A:

Q: Determine the particular solution for y"-4y'-12y=2t^3-t+3

A:

Q: y" - 2y' + y = 4e-t + 2et, where y(0) = -1, y'(0) = 2

A:

Q: Use the reduction of order method to solve the equation y" + 2y' + y = 2e-

A:

Q: y" + 2y' + 4y = 0

A:

Q: Find the general solution of the Bernoulli equation 2yy′= y^2+ t + 1.

A: To solve given differential equation first we solve for rearrange the equation in the form of first…

Q: Obtain two linearly independent solutions valid near x = 0 x(1-x)y" - 3y' + 2y = 0

A: