find the particular solution corresponding to the given initial conditions 1 y – x + 8 y' у — х — 1 y(1) = -2 A) (y – x)² + 2(y – x) = 9x + 3 B) (y – x)² – (y – x) = 18x – 3 C) (y – x)² – 2(y – x) = 18x – 3

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Q: 1.) +y=e+ dx=3e-t 2. .) d- given: x(0) = 0, y(0) = 1 dy-x=0 d+y=1 given a z (0) = -1, y(0) = 1.

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Q: 7. Show that y(t) = c,e¬# +czte¬2# is a solution to y" +4y/ +4y = 0. Determine the constants c and…

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Q: (a) Verify that *₁ = x₂(x3 + U₁), *₂ = x₁(x3 + U₁), x3 = U₂ (x₁(t) = sin(2t), ₂(t) = cos(2t), 3(t) =…

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Q: Example 5.8. Solve du 0 0, ax2 at for (i) u(x, 0+) = f(x), (ii) u(0, t) = 0, t > 0, (iii) u(1,t) =…

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Q: Solve the PDE of the first order и, — и, — 0, и(х,Зх) — 2? и (х, Зг) — Ur – = x

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Q: 1. (Theorem 2.1, Eq. 2.4) By employing change of variables r = ax +y and s=x, prove that the PDE: A…

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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.