In this problem you will use variation of parameters to solve the nonhomogeneous equation y" - 2y + y = -4et A. Write the characteristic equation for the associated homogeneous equation. (User for your variable.) r^2-2r+1= B. Write the fundamental solutions for the associated homogeneous equation and their Wronskian. Y1 = W (y1, y2) = Y19 C. Compute the following integrals. [³ W e^t te^t, e^t Y29 W - dt = 2t^2 J D. Write the general solution. (Use c1 and c2 for c₁ and c₂). dt = -4t Y2 = y cle^t+c2te^t-2t^2e^t te^t (Note: Your general solution will only be correct if it is a general solution to the differential equation.)

Q: Write down two linearly independent solutions of the Bessel equation 16x?y" + 16ry + (162 – 9) y =…

A: The given differentiate equation can be written as:

Q: xy2 y' = ey + sin y dy = dx x+y y' = x2

A:

Q: Classify each of the equations above as autonomous, separable, linear, homogeneous, Bernoulli, or…

A: "Since you have posted a question with multisubparts, we will solve first three parts for you. To…

Q: Solve the homogeneous equation xdy−ydx =√(x^2 +y^2)dx

A:

Q: b. (1+y²)y" + xy' - 3y = cos x solve and show that this equation is non- linear and non-homogeneous.…

A: As per the question we have to use the solution of the given second order differential equation to…

Q: Solve the nonhomogeneous equation? .3. x*y" + x²y" – 2xy' + 2y = x³ In x. -

A:

Q: Find an integrating factor of the form x^ym and solve the equation. (2y² - 6xy)dx +(4xy - 6x²)dy = 0…

A:

Q: Solve by undetermined coefficients. y" – 3y' = 6e – 2e", y(0) = 0, y (0) = 0.

A:

Q: Solve. y" + 6y (y')³ = 0 v(x) = Czei* - 6 b. Czy+y³ = C2+x c. (C2 - y)? + x² =C1 d. y= C2 - In(C,…

A:

Q: Use the integrating factor method to solve 2xy + y = 2x5/2

A: Please find attachment

Q: 1. Find a general solution of the first order equation: y'= 3x²y².

A: The given first order differential equation is solved by method of separation of variable.

Q: Solve (2x – 1)3y" + (2x – 1)y' - 2y = 8x? – 2x + 3 %3D |

A:

Q: 2. 2 Solve (D² +2DD' + D'² -- 2D– 2D')z =sin(x +2y)

A: Given the pde

Q: Find the linear differential equation that is satisfied by y=xe-xsin3x+2e-xcos3x.

A: Let's find linear differential equation.

Q: (2y² + 3x) dx + 2xydy = 0 Determine an appropriate integrating factor (x) or (y) that transforms the…

A: Solution :

Q: Find the general solution of the DE: y’’’ - 4y’ = 32xe^2x - 24x^2

A:

Q: 2. An L: R² → R² linear operator for every (x, y) E R? için L(x, y) = (x - y, r – y) şeklinde…

A: Note:- Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the…

Q: Find the the solution of y' = yx³. O y= x*In c O x4 = In cy O y= In cx4 O x* = y In c

A: So option b is correct.

Q: Solve for y' 4xy+ y² 2x2 –2y

A: The objective is to solve y'=4xy+y22x2-2y. The equation can be written as, -4x+yy+2x2-2yy2y'=0 The…