State Leibnitz's theorem. If V1- x² y =sinx, then prove that (1-x) yn+2– (2n+1) xyn+1=n°yn= 0.

Q: Given z = (e-2) (siny), find dr -2x O-2 e 2² (cos y) O-2 e 2 (sin y) O-2 e 2 (sin y) +e-2 (cos y)…

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Q: d -1 ) Prove that cos 1(x) : dx V1-1

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Q: 7. Prove: sin(t) dt sin(1) + cos(1) 4

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Q: A V3 sin-' (xy/2), Po(1, 1), 12. h(x, y) = tan (v/x) + A = 3i – 2j

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Q: 1 - / sin2r - ycos2r điferansiyel denkleminin genel çöztumt aşağıdakilerden hangisidir? a) Hiçbiri…

A: Consider the homogeneous differential equation y'sin2x-ycos2x=0. Variable separable form:…

Q: Evaluate the integrals

A: First of all use the trigonometric formula that is 1-sin2x=cos2x in the given integral to simplify…

Q: If y = cos ¹ prove Zyy + z = 0. )Z = (1 + i)(2-1)-¹, find |Z|.

A: Here given y=cos-1(z/x). We prove that zyy+z=0.

Q: a. Z1 Z2 = r1 r2 [cos(0, + 02) + j sin(0, + 02)] %3D Z1 =" [cos(0, - 02) +j sin(01 – 02)] b. | | Z2…

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Q: 1 y = e*(C, cos2x + C2sin2x) –xe*sin2x a. 2 b. y = e*(C, cos2x + C2sin2x) +xe*sin2x 1 y = e*(C,…

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Q: (x²+y² 4. If u = sin-1 ( ) then prove that by Euler's theorem, x+Vy. ди X + y: дх ди 3 tan u. 2

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Q: A particle moves along the x-axis so that at any time t, t 2 0, its acceleration is a(t) = -4…

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Q: Eliminate the Arbitrary Constant •y= C, e¨cos3X + C, e**sin3x •y. Ac" + Bxe* y: x*+C,c" + C, e**

A: soln 1 y=Ae2x+Bxe2x    diff with respect to x∴y'=Ae2x(2)+Be2x+Bxe2x(2)…

Q: x = 2 sin-1 1, y = In (1 – r²) (0<1s!)

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Q: Q2 : Express the function r2 +r(sin0 + cos 0) = r² sin² 0 by %3D cartesian form

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Q: sin(nz) b) E: on (0, 2x] n-1 AcoAnA

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Q: au at a²u 28. Solve Əx² U(x, 0) = 3 sin 2+x, U(0, t) = 0, U(1, t) = 0. = where 0 0 together with…

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Q: Solve ", = c²u«» 0sxS1, t20 subject to u (0, t) = 0, u(1, 1) =0 for all t u (x, 0) = 0, u, (x, 0) =…

A: The general solution for the homogeneous wave equation…

Q: sin (21 + 1) dt J cos² (21 + 1)

A: As per our guidelines we are supposed to answer?️ only one question. Kindly repost other question as…

Q: z = 2ev Ве ev-sinx – 3e*÷cosv) find: www a2z a2z az a)- дудх ,b). дхду 4 ax

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Q: 4.1 z + cos(72) -dz, c z(z² +1) with C : |z – i| =.

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Q: (b) Show that, the function u = In(x² + y²) + 2 tan" satisfies Laplace's equation.

A: A Laplace equation is a 2nd-order partial differential equation. This is defined by,…

Q: a) u=r³-3ry² + 2xy + x, D) u= x² - y² +5, c) a= sinh rsing, d) u = e(y cos y + x siny), e)…

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Q: The auxiliary roots of the auxiliary equation associated with a certain HLDE are m=±3, ±3i, + 3i.…

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Q: 4. a. Show that for 0 Va² + sin² a. b. Generalize the result in part (a).

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Q: The special solution to the equation * (D²-3D+4)y(x)= 4sin(2x) Y,(x) = Excos(2x) у, (х) cos(2x) -…

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Q: C) Find a z and of xy" ay (xy2) - -군3 COs %3D

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Q: How do I solve the laplace(u(t-2)cos(t-2))

A: The Laplace transform formula for translation on the t-axis is given by ℒ{u(t-a) f(t-a)} = e-asF(s),…

Q: 2 f(t) = ( tv4t2 + 1, sin(t) cos² (t), t2 + 1

A: As you ask parts b and c. in part b we need to find the equation of the tangent line to the curve at…

Q: ♥ дzu ахбу = сезх созу, Ans: u(x,y) = sinx siny + x² + 2 cosy - #2² X 1 бу исx;#) =X бx U(x,п) =X,…

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Q: du Given u In[y cos(3x²y)1, solve CoS %3D ax

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Q: a. Show that If z=x+ iy where y 1 b. Evaluate: cosh (iz) + sin (2)

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Q: (3 cos t – 1)i + (2 sin t + 3)j,

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Q: ди ди then x +y = u. 31. If u = Jy² - x2 sin-

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Q: Determine an equation for the sinusoidal function shown. 2. 12 21 Oy = 0.5 cos[0.5(x+ x)] + 1.5 Oy,…

A: The general equation of a sin function is given by; y=A cos(Bx+C)+D Where; A→Amplitude of the…

Q: PDE: uf = 2ихх, 0 0 0 0 ВС: и (0, t) — —1, иx(1,t) — 1 3πχ IC: и (х, 0) — х + sin - 1 2

A: Claim: solution for the heat equation: Let us use separation of variables. Let u(x,t)=X(x)T(t).…

Q: - Using Euler's equation, show that- : z fain (K 0)} - z sin Ø z2 – 2zCos Ø +1

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Q: 1. Use Green's Theorem to evaluate [(3ye* -7 sin (3x*))dx + (5x* +2x*y* +8e*-y* )dy, where C is the…

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Q: (a) Prove that dv 1 2 u? + v2 arctan u- + C. 2 u 2, /2/2 ru (b) Prove that I dv du 2 - u? + v2 18 by…

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Q: . и., — и. — sin x сos t, t>0 В.С.: и(0, г) %3D0, 1.С.: и(х, 0) %3D 0, 1,(x. 0) = 0

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Q: Example B Consider the inhomogeneous equation Yk+1 – 2yk coS Ø + Yk-1 = Rx, sin ø # 0, %3D

A: Given           yk+1-2ykcosϕ+yk-1=Rk  ,  sinϕ ≠0       ... (1) where ϕ is constant and Rk is…

Q: Test for exactness and find the general solution of: (cos2y – 3x²y²)dx + (cos2y – 2xsin2y – 2x³y)dy…

A: To solve the following differential equation

Q: 1. Eliminate the parameter tgiven x = t – 3 sint and y = 2 + 3 cos t.

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Q: Determine cı and c2 so that y(x) = c1 sin 2x + c2 cos 2x + 1 will satisfy the conditions y () = 0…

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Q: a. Show that W[5, sin2 t, cos(2t)] = 0 for all t by directly evaluating the Wrosnkian.

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Q: 8) Prove: Prove that a general solution of the equation y" - y = 0 is given by y = c cosh t+cz…

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Q: Let y= c1 cos 2x +c2 sin2x be a two-parameter family of solutions of the second-order DE y"+4y=0.…

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Q: Solve the trigonometric equation V3tanx-secx = 1 exactly on the interval 0 <x < 2n. 2n =0. 3 X = - t…

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Q: The auxiliary roots of the auxiliary equation associated with a certain HLDE are m=±3, ±3i, ± 3i.…

A: Solution is given as below:

Q: The solution of the DE (1+ cot'x)y' = cscx coty is %3D None of these siny + In|cosx| = C cosx + In…

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Q: 3. у" — у' — 2у %3D5 sin x y(0) = 1, y'(0) = -1 -

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