Problem 3. Find the general solution of the homogeneous system below. Describe the solution in parametric vector form. ₁ + 2x2 3x3 = 0 4x17x29x3 = 0 -15x2 + 12x3 = 0
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- Find a system of two equations in two variables, x1 and x2, that has the solution set given by the parametric representation x1=t and x2=3t4, where t is any real number. Then show that the solutions to the system can also be written as x1=43+t3 and x2=t.Consider the system of linear equations in x and y. ax+by=ecx+dy=f Under what conditions will the system have exactly one solution?Find a system of two equations in three variables, x1, x2 and x3 that has the solution set given by the parametric representation x1=t, x2=s and x3=3+st, where s and t are any real numbers. Then show that the solutions to the system can also be written as x1=3+st,x2=s and x3=t.
- Now consider the case when the parameter varies slowly in time ,that is consider the system x'=a+x-x^3 and a'=-bx when b is so small. Sketch a typical solution to this system.In following problem, two linearly independent solutions and are given to the associated homogeneous equation of the variablecoefficient nonhomogeneous equation. Use the method of variation of parameters to find a particular solution to the nonhomogeneous equation. x2y" + 2xy' - 2y = x2 , y1 = x-2, y2 = xI am struggling to find the solution for the system x(t) and y(t), given the information highlighted in green. Can you please explain the steps to better understand?
- Consider the non-linear system of equations: f1(x,y)=xy f2(x,y)=x(1-y) a) What are the roots for this problem? b) What is the Jacobian if we write our unknown vector as [x,y]? c) When I try to solve this with Newton-Raphson, I run into a problem. What happens?Calculate analytically the solution to the non-homogeneous system: x' = Ax + Bu y = Cx + Du A = [ 1 1; 0 2] x0= [1;0] ı sent you question's image. thank you..2. Use the method of variation of parameter to solve the nonhomogeneous system?′=??+?(?)where,?=⌈12 32⌉; ?(?)=⌈2 ?⌉?2?