Use the eigenvalue method to find the solution of the following system with given initial conditions. x₁ = x₁, x₂ = 8x₁ — 4x2; x₁ (0) = -2, x₂ (0) = 3. Evaluate the solution at t 1 and select the most approximate values. ° [*)] = 0.051 0.446 O ° [21(3)] = [007] 0.673 0.043 ° [2]-[978] (1) 0.776 (1) 0.033 ° [28]-[88] = (1). 0.561

Use Euler's method to obtain a four-decimal approximation of the indicated value. Carry out the recursion of the equation Yn+1=Yn+hf(xn¹ Yn) by hand, first using h = 0.1 and then using h = 0.05. y(0.2) y(0.2) y' = x + y², y(0) = 0; y(0.2) (h = 0.1) (h = 0.05)

give me the solution of   y'' - 2y'- 2y = 0

#1 Solve the following non-linear equations manually using: a) Bisection Method (5 iterations)

Determine all the solutions. Find the solution that passes through the orgin y'= 2x + y + 1 x + 2y + 2 X

Find the general solution of the following DE in explicit form. y'=3+2/y-3x +12.

Consider the following nonlinear equations. fi = sin(6x,)+ cos(4x,)–1.5x, = 0 f2 = e* +6x, +4x, = 0 f = x, -x, +3x, = 0 %3D Use the initial values as [1,1,1), solve the nonlinear equation system.

Suppose that y1 (t) and y2 (t) are fundamental solutions of the equation L(y) = 0 and let y3 (t) be a solution of L(y3) = b(t) 0, where L(y) = y' + a1 y + ao y. Choose all the statements below that are correct. The function Y1 + y2 is solution of the homogenous equation L(Y) 0. The functions &y1 + c1Y2, for C1 an arbitrary constant, is a general solution of the equation L(y) = 0. The function 7 yı – 7y3 is solution of the homogenous equation L(y) = 0 U The function 7 y1 + Y3 is solution of the homogenous equation L(y) = b. The functions C1Y1 + C2Y2, for C1, C2 arbitrary constants, is a general solution of the equation L(y) = 0. The function 3 y3 is solution of the homogenous equation L(y) = b. U The function 3 y1 is solution of the homogenous equation L(y) = 0. The function Yı – Y3 is solution of the homogenous equation L(y) = –6.

Find all solutions of the form y = erx for the equation y''−y'−2y = 0. Then write the most general solution that can be made out of them.

Find the general solution of