Use the elimination method to find a general solution for the given linear system, where differentiation is with respect to t. x' = 6x -y y' = 6y - 9x Eliminate x and solve the remaining differential equation for y. Choose the correct answer below. гу. O A. y(t) = C, e - 31 + C2 e - 9t B. y(t) = C, e 3t + C2 e 9t OC. yt) = C, e 31 + Czte 3! O D. y(t) = C, e 91 +Czte 9t O E. The system is degenerate. Now find x(t) so that x(t) and the solution for y(t) found in the previous step are a general solution to the system of differential equations. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. x(t) = O B. The system is degenerate.

Q: Determine if the equation is exact, then if it is exact, find the solution. (2x+3)+(2y−2)y'= 0…

A:

Q: Choose the correct answer If x2 + y2 = 9, then y'=...  -y/x  y/x  -x/y  x/y

A: We have to find y'

Q: Solve for the exact first order differential equation. Find the appropriate integrating factor and…

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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: Determine the value of k that will make y = 2cos(2x) a solution to ky - y" = y. Ok = 5 Ok=0 Ok = -3…

A: Step 1:​y=2cos(2x) is a solution of ky−y′′=y.​Step…

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.