Exercise: Find the general solution of the given DEs 1. 12y" – 5y' – 2y = 0 2. y" + 2y" – 5y' – 6y = 0 %3| 3. y(4) – 2y" + y = 0 - %3D

Q: Solve y" – 2y' – 3y = 3t² – 5 using the Method of Undetermined Coefficients.

A:

Q: You have been given the following: x=y-x+t x(0)=6 y(0)=2 y'=y Solve it and write you answers in the…

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Q: Find a particular solution, y,(x), of y(ª – y" = 12e3 – 5x + 2. -

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Q: Select all equations that are equivalent to a-6z 16. a + 6x 9 0 O b a + 6x +9 = 16 Oc a+6x + 9 = 25…

A: Solution:-Given equation,     x2+6x=16  —1let us see and solve each option given,a…

Q: 1. Given h(x) = 5x² – 3x – 2 which pair of the equations below are possible - equations for f(x)and…

A: we need to find the subtraction of two real valued polynomials.

Q: Find the solution of x = X₂ JED -6 where u(t) = 2 and x(0) = [1 -1]. 11 0 JUCE + u(t) (10)

A: The problem is solved using the concept of eigen value and eigen vector.

Q: Solve y" – 4y' + 6y = 8(t – 3), y(0) = 0, y'(0) = 0. -

A: Use Laplace table.

Q: dy 21 +y = xy". Solve: dx Ay20 = x + 1+0 1 + Ce" 20x 20 -20 O B.Y ** = x + + Ce21x 20 1 Oc.y20 +Ce…

A:

Q: 3. Find all solutions to the equation (D² – 3D + 2)y(x) = 2e3ª.

A:

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.