Distinct Real Eigenvalues
In Problems 1–12 find the general solution of the given system.
8.
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First Course in Differential Equations (Instructor's)
- Question 9 Find all the roots of z3 – 3(5 +j) = 0 and give the answers in rectangular form. Question 10 Use Crammer's rule to solve the following linear system for y only. 2x – 3y = 3 – z 4x +y = -4 = 3y + z-2 İLIFE Digitalarrow_forwardProblem 16 (#2.3.34).Let f(x) = ax +b, and g(x) = cx +d. Find a condition on the constants a, b, c, d such that f◦g=g◦f. Proof. By definition, f◦g(x) = a(cx +d) + b=acx +ad +b, and g◦f(x) = c(ax +b) + d=acx +bc +d. Setting the two equal, we see acx +ad +b=acx +bc +d ad +b=bc +d (a−1)d=(c−1)b That last step was merely added for aesthetic reasons.arrow_forwardPart III Obtain the particular solutions of the following: d. y(2x* - xy + y* )dx –x (2x – y)dy =0,arrow_forward
- 4. (S.10). Use Gaussian elimination with backward substitution to solve the following linear system: 2.r1 + 12 – 13 = 5, 1 + 12 – 3r3 = -9, -I1 + 12 +2r3 = 9;arrow_forwardUse (1) in Section 8.4 X = eAtc (1) to find the general solution of the given system. 1 X' = 0. X(t) =arrow_forwardExercise 3.6.1. Find the general solution for the system -3 x = ( 23 ) x + cos(2t) ( _ )+(²).arrow_forward
- 5. Solve the following linear system: dX dt with the initial condition = [83] X (0) = -3 2 X Garrow_forward3. 2хydx - (3xу + 2y?)dy %3D0 o (x - 2y)*(2x +y) = c (х — у)"(х + у) %3 с (х + 2y) (2х- у)* %3 с (x – 2y)* = c(2x + y)arrow_forward[6 10 12 4 10 Find the complete solution x = xp + xn to the system 2 4 'NN' 2 8 X = 16arrow_forward
- . Find the general solution of (x + 3y – 4)dx + (2x + 6y – 8)dy = 0 %3D *+y = C b. 2x + y = C c. x + 2y = C d. x - 2y %3D Сarrow_forwardProblem 2 Show whether the two equations y₁ = 12e and y2 = 1.2e are independent or dependent using the Wronskian.arrow_forward4. Solve the system dt -1 with a1 (0) = 1 and 2(0) = -1.arrow_forward
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