Q: solve using the appropriate method. y' + (tan x)y = cos2 x, y(π) = 2

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Q: cos z) dz 4 5.

A: Given: - The indefinite integral is, ∫e2zcos14zdz To find: - The solution of the given integral.

Q: Express æ = 3t, y = tan-'(t4 + e') in the form y = f(x) by eliminating the parameter.

A: Given : x = 3ty = tan-1t4+et

Q: Solve for the general solution of (D² - 1)y = sinx using variation of parameters

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Q: Use the method of variation of parameters to determine a particular solution to the given equation.…

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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: Solve the given DEQ by undetermined coefficients. y" + y = 2x sin x

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Q: Find the y sec! (+) %3D

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Q: solve using linear (y-cos2x)dx + cosxdy = 0

A: Topic = Differential equation

Q: cos(T/x5) dx 16

A: Given that: ∫cos(π/x15)dxx16

Q: y = e2* sin 2x + e3* cos 2x

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Q: Find the general solution to y" +y = x sinx

A: We are given second order non homogeneous linear differential equation with constant coefficients.…

Q: Find the solution of the given equation y'''+y'=tanx using Variation of Parameters

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Q: Solve the equation siny(X+siny)Dy+2x²cosydy=0

A: Consider the provided question, sinyx+sinydx+2x2cosydy=0sinyx+siny+2x2cosydydx=0…

Q: Se" cos 2t dt ,7L

A: integration.

Q: Solve for y in equation y e" sin x + e cos x - y+ C.

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Q: Q3) find the soluation of differention equation 2) y' sin 2x = y cos 2x

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Q: 1. Solve, using the method of variation of parameters: y" + y = sec 0 tan 0

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Q: 2x – sin y y' = x cos y

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Q: Solve the D. E J+gtanx = sin ex

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Q: The equation of motion of a body performing damped force vibration, Is given by t 5dx +6x = Cos t,…

A: Given DE is d2xdt2+5 dxdt+6x=cost also given conditions are x(0)=0.1 and x'0=0 solve the equation

Q: Verify that (e* sin y +3y)-(3x- e* sin y)y' = 0 is exact. Then solve the equation. 5.

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Q: Solve this DE 1. dy/dx+secx(y-2sec3x+2sec2 xtanx) + y cotx = 0

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Q: Find the solution of the equation 200 az a²z + cos y Əx² Əy² which tends to zero as x→∞ and has the…

A: Given differential equation∂2z∂x2+∂2z∂y2=e-xcosy. The objective is to find the solution of the…

Q: Solve the DE using Variation of Parameters: y"+y = sec' x %3D

A: Given  The differential equation using variation of parameters. y''+y=sec3x

Q: What is the dependent variable in the equation dr + (2rcot0+ sin 20) d0 = 0?

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Q: Solve (D² - 2D + 5) y = sin (2x) + 17x cos (2x) — 15x -

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Q: Find the general solution to the equation: y' = y sin(2x + 3) .

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Q: y" + y = sin t

A: Explanation of the solution is given below...

Q: dy Solve sin -1 | = x +y dx,

A: Sin-1(dy/ dx) = x+y => dy/ dx = sin(x+y).

Q: cos-(siny) dx dy = -29

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Q: Construct an equation such that y = = C1e3z cos x + C2e3ª sin x is its general solution.

A: To determine the differential equation from the solution  Check the number of constant in the…

Q: Find the value of zrr at the point (0, 3, 2) where x?y? + z2 – cos(xyz) = 10. -

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Q: Write the general solution to y= arcsin 1. Oy=+2 tk Oy=tk Oy= T ak

A: Given :y=ascsin(1)

Q: dy 2y + cos dx ||

A: As per our guidelines we only solve one question and rest of the question will be reposted.

Q: Use Method of Undetermined Coefficients: y" - 2y' + 5y = 4e*cos2x +x?

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Q: Find the solution of d2y/dx2 +4y=sin3xx+cos2x

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Q: Use trigonometric substitutions to find dx. V1-

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Q: Solve the equation [cos (2y) - (3x^2)(y^2)]dx +[cos (2y) - 2x sin 2y - (2x^3)(y)]dy = 0

A: To solve the given differential equation. First we check whether the differential equation is exact…

Q: . Obtain in two ways the general solution of (r+ sine – cose ) dr+r(sine + cose ) de = 0

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Q: Solve the differentual equation y'(sinh 3y - 2xy) =y^2

A: y′ =y2−1sinh(3y)−2xy  Exact Differential Equation An ODE M(x, y)+N(x, y)y′=0 is in exact form…

Q: Use the method of characteristics to solve the first order equation Ug – 2uy = 3 with u(x, x) =…

A: Method of Characteristics and General Solutions: The general solution of the quasi-linear equation…

Q: Solve (sin23x)dy= dx cot3x + C 3 cot3x O b. y= 3 sec3x O C. y = O d. y = sec3x + C 3

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Q: i) Solve: (1+ yNdx = (tan-y- x)dy. %3D

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Q: tan y dy 1-tan2,

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Q: Solve using any method: y" + y = tan x, 0<x< π/2.

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Q: Find y' at the point (4, 4) where x sin(x² – y²) + 13 = x² – 3. -

A: y = f(x) g(x) Then y' = f'(x) g(x) + f(x) g'(x).

Q: c) Se- sin(4t) dt

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Q: 6y' = y*sinx У (0) — 1

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