Solve the non-homogeneous heat equation U = 2urz +e2" sin(x) u(0, t) = u(T, t) = 0 u(x, 0) = – sin(2æ) + 4 sin(3x) 0 < ¤ < T, t > 0 t> 0 0 < x < T %3D

Q: dy/dt= y(y-0.5)(y-3)(sin(t2)-2) Determine the equilibria.

A: In this question, we Determine the equilibria. To explain why the Existence and Uniqueness theorem…

Q: アrova solution to if ulx,t)= (sin (x- 6 )-Sin (x+6)) tion equa %3D

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Q: Find the differential and evaluate for the given x and d/x of the function, y = tan x, x = 0, dx =…

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Q: y" + 4y' + 5y = 50t, y(0) = 5, y'(0) = −5 a. e 2t (13 cost + 11 sin t) + 10t² - 8 b.e-2t (13 sint +…

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Q: (3e* sin(y) + y)dx + (2x + e* cos(y))dy = 0 not exact

A: Que is not clear though. We Shall check exactness for the given differential equation. If you have…

Q: Find the solution Py = ²84, u a 81² ul₁=0 = sin ³7.x, ди du |-o = x(1 − x) (0 < x < l), u(0, t) =…

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Q: y" +2y' = 3+ 4 sin(2t)

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Q: Find y @) y ² y's SX-2 Sin (x) b) 2 Y = 2 cos (x)-x

A: To find the derivative each of the following functions. (a) y=5x-2 sinx (b) y=2 cosx-x2

Q: V ss Vst Vts Vtt || || 11 11 V sin(2s² - 4t²)

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Q: Find the general solution of the nonhomogeneous equation y4) + 2 y "+y=cos( 3 x) + 2 1 a) y =C,…

A: We will find out the required solution.

Q: What is the integrating factor of (1 + cos x) y' = sin x (sin x + sin xcosx sin x 0 1 + cos x CSC X…

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Q: Find y' where y = 8 cos-1 (sin (19 z)) – cot-1 (14 z) Answer: 14 y' = -152 1+196 z2 -152 cos(19 z) +…

A: This question belongs to derivative of inverse trigonometric function.

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.