Let u be the unique solution of where (x, t) e (0, 1) x (0, 00),u(x, 0) = at ax? sin Tx, x e (0, 1) u(0, t) = u(1, t) = 0t e (0, 0) Then which of the following are true? %3D (a) 3 (x, t) e (0, 1) x (0, 0) s.t. u(x, t) = 0 (b) 3 (х, t) € (0, 1) x (0, оо) s.t. ди (x,1) D0 (c) The function e'u(x, t) is bounded for (x, t) e (0, 1) x (0, 0) (d) 3 (x, t) e (0, 1) x(0, 0) s.t. u(x, t) > 1

Q: Q.2) The basts of the equatioon y'' + y" = 0,are: b) 1,1.e a) 1,1.e c) 1, x,e²* d) 1,x.e" 0 about

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Q: Find the general solution of 2ey cos 2x dx + (ey sin 2x + 3y sec2 y2)dy = 0. a. e sin 2x +y tan y? =…

A: This question is related to differetial equations, We will solve it using given information.

Q: If r(2) = sin(z² – 10z + 16), find r' (z) =

A: Since, we have been given that r(z)= sin(z2-10z+16)Our Aim is to find r'(z)=?

Q: The solution of (e +2ay) daæ + (2 cos 2y+ 2x?y) dy is given by (A) e" + a?y² + cos 2y = c (B) e +…

A: The given equation is; (ex + 2xy2) dx + (2cos2y + 2x2y)

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A: Given differential equation is  1x2+1+cosy-2xydx-xsiny+x2dy=0 This equation can be written as…

Q: " + y = 12 cos 2x - sin x. A. " + y = sin 3x +4 cos x. A

A: Given: y''+y=12cos2x-sinx

Q: (1) (II) 10 F. 10 +t 10 10 -10 -10 (II) (IV) 10 10 斗t 10 t 10 -10 -10 a) y = 10e-t/2 cos 2nt b) y =…

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Q: 1. Find dy/dx a) y = In (2x² – 3x) %3D b) y = [e" dt ) d) y = In|sec(x)+ tan(x) e) y = 7std*) S)y =…

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Q: Is the function y = Cx? a solution to the ODE y" – xy' + y = 0?

A: Using Derivatives.

Q: Q1: Find 1) e (3 + e6t)2 2) l {e-3t (t + 1)²}

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Q: a) Find a function ƒ such that f'(x) = 4x² – 2x – 1 and f (-1) = 2 %3D b) Find the function g such…

A: Given: f'x=4x2-2x-1, f-1=2 for finding functionfx, we integrate f'x so,…

Q: Solve: [xcos² (y/x) − y]dx + xdy = 0 4lnx + sin(2y/x) = C 2y 4lnx + sin(2y/x) = C x sin(2y/x) = C +…

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Q: If u(x, t) = D1 fn(t) sin(nx) is the solution Utt – 9ura = 2e2t sin(3x) + e-2t sin(4x) u(0, t) = 0 =…

A: Given: ux,t=∑n=1∞fntsinnx is the solution of the PDE…

Q: Find VV when (a) V = x² + y + ? y. (b) V = z sin (c)V = e+y+tz.

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Q: Find the general solution of y''' − y'' − y'+ y = 1 + sin x + sin 2x + ex

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Q: f(t) = e2t cos 5t S- 2 (s – 2)² + 25 2s + 4 s(s² + 4) %3D Ans. f(t) = (sin t –- cos t)² %3D Ans.

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Q: Prove this equation by deriving F(x, t) =X(x) Y(y). Please show full steps OF OF 2. +2x- =D0 Ditebak…

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Q: Solve vxx + vyу %3D ху ,х € (0, п), у € (0, п ) v(0, y) = 0 v(п, у) %3 sin2y vх, 0) — sin3x v(x, 7)…

A: Given: vxx+vyy=xy   …1, x∈0,π, y∈0,πv0,y=0vπ,y=sin2yvx,0=sin3xvx,π=0 We have to solve equation (1).…

Q: dx 2 sin X dy ☺ Cym) de + $cx-) dy =o $ (x-1) dy= o

A: (2) sin(x)dx+y2(x-1)dy=0⇒ sin(x)dx=-y2(x-1)dy⇒sin(x)(x-1)dx=-y2dyIntegrate both sides we…

Q: The solution of у" + у 3D 0, у(0) — 0, у'(0) — 1 is y(a) = (A) cos x (B) sin x (С) 1 — е ӕ (D) 1– eª…

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Q: 17) Let f(x) : Find a %3D X - 9 function y = g(x) so that (f •g)(x) = x. %3D

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Q: Answer The solution of the ODE * 1 1 sinxy dx + sinxy dy = 0 y S- sin xy dx + g (y) S- sin xy dx + g…

A: We will use simple algebra of numbers and basic method find solution of this differential equation

Q: 23-4x-8 Integrate: 2E+4) dx 1)(r²+4)

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Q: Q5) Solve the equation with y (0,1) = y (1,1) = 0 y (x,0) = sin x ! = 0,0 sxSI 8. ду (х .0) and…

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Q: Can you explain how all A B C D terms are calculated

A: Solution of the given question is like as

Q: f, (3,5) and fy (3,)us(«, y) = |and f, (3,) if f (x, y) = (b) Find x² sin(y) – Ax-3 10 CLO-2 Where A…

A: The given function is  f(x, y) = x2. siny - Ax-3

Q: x(t) 9 sin (t) A y(1) 4 cos (t) 9 sin² (1) 4 sin? (1) x(1) B y(1) %3D c (1) = 4 + 9 sin (4) DY) = 9…

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Q: Find the general solution dy + cos(x)y = cos(x) dx O y = 1+ ke-2 sin(x) O y² = 2 sin(x) + c y =…

A: Given differential equation is dydx+cosxy=cosx........1. We have to find the general solution of the…

Q: If z = x2 – y2 and x t cos 2r and y = r sin t, then %3D a2z is ar2 (A) 2 cos (2r) + 2r? cos?(t) –…

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