Consider the following pairs of differential equation that model a predator-prey system with populations x and y. In each case, carry out the following steps.a. Identify which equation corresponds to the predator and which corresponds to the prey.b. Find the lines along which x'(t) = 0. Find the lines along which y'(t) = 0.c. Find the equilibrium points for the system.d. Identify the four regions in the first quadrant of the xy-plane inwhich x ' and y' are positive or negative.e. Sketch a representative solution curve in the xy-plane and indicatethe direction in which the solution evolves. x'(t) = -3x + 6xy, y '(t) = y - 4xy

Q: FIND THE GENERAL EQUATION OF THE FOLLOWING SOLUTION: y" = 12 %3D A.

A: A) The differential equation is given as y''' = 12 On integrating both sides , we get ∫y''' = ∫12y''…

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A:

Q: You are given a first-order D.E. = x2 + y³ . Suppose the solution y(x) satisfies the initial dx…

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Q: Solve for a linear equation? P(t)y'' + Q(t)y' + R(t)y = S(t)

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Q: • ex+y -2y-2=Ce e2x+y +2y-2%3DCEY e2xy -2y+23DCEY

A:

Q: 1. Describe each of the following equations, giving its order and telling whether it is ordinary or…

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Q: Find a constant solution of y′ = t2y - 5t2.

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A:

Q: Show that a linear equation dy a(x)- + b(x)y = c(x) d.x %3D is exact if a' (x) = b(x).

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Q: 3. Solve the DE: Y'=e2x+ 3y.

A:

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Q: Find a slope of the solution of y' = t – y at (3,1).

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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.