Solve Non-Exact DE: udv – v(1 + v cos 2u)du = 0

Q: dy 13 %3D - dn Solve this by using Bernoullis eajuation?

A: Given differential equation is: dydx=y(xy13-1)dydx+y=xy141y14dydx+1y13=x                         (1)…

Q: Show that u(x, t) = 4 tan-1 I-ut ev where v is constant, is solution of Uxz – Utt = sin(u)

A: To check the given solution satisfy the given partial differential equation, substitute the solution…

Q: Solve the given differential euation: + rtan 0 = 6cos0 r = (60 + C') cot0 )r= (60+C) sin® r = (60 +…

A: Explanation of the answer is as follows

Q: find the area bounded by the given curves.

A: Given curves are  y=2sinx and y=sin(2x) , x lies in 0 to pi The curve y= 2sinx is above the curve…

Q: I. Solve the heat o at with lot) - (2,t) 3TX 8TX aud Ulxio) = lo + 5 Cos - 3 Cos *

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Q: 2 Solve this Di fferential equat ion by applying ( variation paramet ers) 4+y = y+y%3DSE c x

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Q: use two and three points of Gaussian-Quadrature method to Find 1 = e" e(1+sinx) dx

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Q: sin xdx 3 S cos° x

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Q: Find a particular solution to y" + 36y = 24 sin(6t). %3D

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Q: (e² sin*(2r)' 21² +1 , y = In

A: Use the lograthim rule of derivative and than with the help of chain rule calculate the derivative…

Q: T T 68. y = sin 3 + 4 %3D -

A: Given data:     The given expression of the function is: y=sin(-πx/3 – π/2)+4.     (a) The general…

Q: Solve the following equation by using separation variable method: u(0,t)= u(6,t)=u(x,0)=0 u, (x,0)=…

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Q: aw Q:3) Find ду if w 2u' v+ In(5v) , u=x+y & v=e"siny

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Q: : Find the length of the cardioid r = 1 + cos 0 0 < 0 <T

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Q: -2 cos(6t) dt J (10+4 sin(6t))²

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Q: Reduce to first order and solve 1> 2xy"= 3y' Cos n ii) xy"+ 2y'+zy = 0, Y, = ニ

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Q: | cos xdx sin x

A: Given query is to find the solution o the integral using substitution.

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

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Q: Given the acceleration and initial velocity of a body moving along a coordinate line at time t, find…

A: The acceleration of a body moving along a coordinate line at time t is given by: a(t) = 8 sin(4t)…

Q: -2 Ssin®(3x)cos(3x) 5 dx

A: Given, ∫sin53xcos3x-25dx We have to find the integration.

Q: The equation (tan?x+3y²)sec?xdx+(3tan?x+y²)dy= 0 can be solved by A Bernoulli's Equation B…

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Q: 9. TC/2 (3 sin² t cos ti+ 3 sint cos² tj + 2 sint cost k)dt

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Q: x = a(0 – sin 0), y = a(1 – cos 0). %3D %3D urve followed by the particle as a function of 0.

A: The given parametric equations are, x=a(θ-sinθ)...............(1) y=a(1-cosθ) .............(2)

Q: Solve the heat equation in the glass bar U; = 0,0034ux u(0, t) = 0 %3D u(24r , t) = 0 u(x, 0) = 16…

A: In this question, we use the separation of variable method. and then put x=8π

Q: 2: Clasafy ad Solve The fllowing diffrential equatóns dy -2x e + + 4. Sinx フス2 フィ* + (6 y = 6x°1ox…

A: The general solution of an ordinary non homogeneous differential equation is the sum of…

Q: cos²x sinx dy + (y cos³x − 2)dx = 0

A: Given problem:- cos2(x) sin(x) dy+(ycos3(x) -2) dx=0

Q: (cos t)y" + (sin t)y' – ty = 0,

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Q: SV1- x2 sin-1x dx

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Q: Solve for the General Solution ds 5s = dt te 5t sin t %3D

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Q: T/4 cos vt dt COS T2/36 Vt sin vt

A: Integration by substitutions

Q: Let y, be a solution to y" + zy +r'y = cos (z) and y, be a solution to y" + zy' + z*y = sin°(z).…

A: Given that y1 be a solution of y''+xy'+x2y=cos2x and y2 be a solution of y''+xy'+x2y=sin2x. That is,…

Q: The equation (tan?x+3y?) sec?xdx+(3tan?x+y²)dy=D0 can be solved by A Bernoulli's Equation DE with…

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Q: U + ru, =x u(z,0) = sin(87x) cos(90r). IE R, t> 0,

A: Given ut+xux=x2 By Lagrange's method , we get dt1=dxx=dux2 By equation (1) and equation (2) , we get…

Q: Use the d'Alembert solution to solve 1 0u 9 dx2' u(x, 0) = cos? x, u(x,0) = e"+1. -0 0, t > 0,

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Q: dt 1. cos (2 sin 2r) V1-4r

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Q: cos 2y dy sin y

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Q: which u-sub will help integrate this? A. u = dx 11 [arctan(x)]" dæ = [9 + 12 cos(x)]" B. u 9+ 9x2 C.…

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Q: Solve the DE by Variation of Parameters (D³ + D° = 2D) y = 4e¯= cos z -2x COs I y (0) = 0.4, y' (0)…

A: The differential equation is D3+D2-2Dy=4e-2xcos x with the initial condition y0=0.4, y'0=-0.4,…

Q: (cos 2y)-3'y de+ [{os 2y)- 2.(sin Zy) - 2xyl dy 0

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Q: et cos(e') dt = (b) +C 3+4 sin(et) 3/4 sin-1 (c) (승교) dx = 16x?

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Q: Calculate $ |z|=1 z²e¹/z cos(1/z) dz.

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Q: I d²u dv² tan v sec“ V

A: Find your answer below

Q: Integrate f,-¿ S=; cos x²dx dy =1 (x= 1 y=0 Jx=y Select one: a. cos1 b. .5cos1 C. sin1 d. Non of…

A: We will find out the required value of given integral.

Q: T/2 %3D cos (2wt + O, + ©z)dt = 0 -/2

A: The solution are next step is

Q: dr Solve the given differential euation: + rtan 0 = 7cos0. de %3D r = (70 + C') cot0 Or = (70 + C)…

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Q: 2. Prove that, V{(sec 0 - 1)/(sec 0 + 1)} cot 0. = cosec e

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Q: A particle travels along the helix C given by 7 (t) = cos ti + sin tj + 2tk and is subject to a…

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Q: Cos Vt dt 3. Evaluate

A: The integration of the given integral is; Cos√t/√t.

Q: Find the solution by separating variables. Utt = 4uxx (u (0, t) 3D и(2,t) 3D 0 u(x,0) = sin³(,) for…

A: Given a hyperbolic equation, utt=4uxx with initial and boundary conditions as follows,…

Q: The integral . (cos(3x))'sin(3x)dr under the change of variable u = cos3r becomes v u'du. 9/29

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