The functions plotted below are solutions to one of the following differential equations. Which one? Is a positive or negative? 4 -2 -4 -6 -8 1 2 4 7 (a) y" + ay' + 4y = 3 – 3x (b) y" + ay' + 4y = 3e2 (c) y" + ay' + 4y = sin 2 (а) у" + аy' + 4y 3D 2? + Зх — 4

Q: 0. Compute the exact values of the roots of the auxiliary equation, and construct the solution of…

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Q: Check that the indicated function is an explicit or implicit solution of the given differential…

A: Consider the differential equation dydx=xy+3x−y−3xy−2x+4y−8 Hence,  dydx=xy+3x−y−3xy−2x+4y−8…

Q: a) dy dx xe ex²+ y(0)=1

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Q: Please answer 10A and 10B.

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Q: b. Write down the equation describing the solution's limiting behaviour as t → ∞.

A: If Q is a function of the variable t, when the input t changes, the output Q also changes. If the…

Q: Make the Nonexact differential equation xy dx + (3y2 + 2x2 – 20) dy = 0 to an exact differential…

A: The solution is given as

Q: 2. Solve the given differential equations by the indicated method. a) y" +4y' + 5y = 4e + 15x - 2…

A: Note:- As per our guidelines, we can answer the first part of this problem as exactly one is not…

Q: 3. a) Use the substitution u = -x+3y to solve the differential equation. -x+3y)y'= 1 b) Clearly…

A: After substitutions, separate du and dx.

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.