(a) Explain what is a fundamental set of solutions of an n-th order homogeneous linear differential equation. (b) Each fundamental set of solutions of the equation dy +x dx6 d¹y d²y +24 dr4 dx² 2e-2 da 8y=0 is composed of (i) five solutions (ii) six solutions (iii) infinitely many solutions ■ Check the box with the correct answer. Explain your answer. 20

Q: 2 1.5 dx dt -1.5 -1 3 with x(0) -2 ||

A: Laplace transform  Partial fraction  Inverse Laplace transform

Q: (04-16) y = x#+ x+ 1

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Q: d5y 3) d²y d*y d3y + 13 dx3 13 dx2 dy + 36 dx + 36 y = 0 dx5 dx*

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Q: [1] Solve for the GS of (D4-5D³+9D²-7D+2)y=0

A: By Bartleby policy I have to solve only first one as these are unrelated problems.These are…

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A: (d) x" + 4x + 5y = t2 . . . . . . (1)        y" + 5x + 4y = t + 1 . . . . . . . . (2)        (1)…

Q: Solve the Differential Equations d4y/dx 4 + d2y/dx2 – 2y = 0

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Q: xux-yuy+y2u=y2x find the general solution

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Q: Solve the general solution of the differential equation (D4 + 2D3 – 6D2 – 16D -8)y = 0

A: General solution of the differential equation

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Q: differential equation .2x 2

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Q: ach in parts (b) and 2. Find the 2 x 2 system of lincar differential equations whose general…

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Q: Solution (28 + x) is the particular solution of which differential equation? O a. (D5 + 4D³ )y = 7 +…

A: Here we go in the reverse direction.

Q: Solve each of the equations. Integrating Factors (4x2 – 3y² – 3y² + 2) dx + x (2.x – 2y + 1) dy = 0…

A: ANSWER:- From the given Integrating Factors (4x2 – 3y2 – 3y2 + 2) dx + x (2x – 2y + 1) dy = 0

Q: Q- For the system shown below find the differential equations that relates ( R. ll C. ep (T i=…

A: By using KVL method, eq=Ra+sLaLa+ebea-RaLa-LadLadt=eb...1and T=Jd2θdt+bdθdtT=KEIaeb=KEdθdt

Q: The population of a community is known to increase at a rate proportional to the number of people…

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A: Given differential equation: We have to solve the given differential equation by using…

Q: Given that y₁ (t) = et, y₂(t) = tet and y3(t) = e-2t are linearly independent solutions of the…

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