particle is moving with the given data. Find the position of the particle 8x7 v(x) = 2 cos r - 4x2, s(0) = 3

Q: dy 4. x - y = x² sin x dx

A:

Q: 5. Find : 60 y= (b) y = cos (11x³ + 5x). dx

A: SOLUTION-

Q: (3t+t²)sin (2t)dt

A: We have to integrate the function        (3t + t2)sin(2t)

Q: y' 5y t²-4 + cos t = = ty

A: Hints: Here we need to obtain whether the given equations are linear or non-linear and homogenous or…

Q: 2y у'+ — х?у? sin x %3D

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Q: J cos 3x cos 4x dx :

A:

Q: Using Variation of Parameters 4y''+4=cos-1x

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Q: + b¬ + cx = 0 dt lution given by: - (A sin ßx + B cos ß.

A:

Q: Determine whether the equation is exact. If it is exact, find the solution. (e*siny + 4y)dx - (4x -…

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Q: Determine the type of equation and find a general solution. dy/dx = (sinx + cosx)/ (y^2-1) show…

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Q: C) Find the equation of tangent to the curve 4x +9yi = 36 at the point (3 cos 0, 2 sin 0).

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Q: Exumple: Solue-the ditfereutial equation dy 2 dey

A: The differential equation is given as x2d2ydx2-3xdydx+5y=0                       (1) We will solve…

Q: cos2x a) -.dx,b) xe*. dy Į sin2x. [In(sin2x)]² + sin2x 0.

A:

Q: x fare cos = dx 2

A: Indefinite Integration

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: Obtain the general solution by separating variables. SHOW YOUR SOLUTIONS. tan2y dy = sin3x dx

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Q: +3x2 b. Find (y)? = sin³(cos³(* *3*)) %3D dx 2

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Q: solve following differential by finding an appropriate integrating factor cosxdx+(1+2/y)sinxdy=0

A: Solution -  We have the given expression as -  cosx dx + 1+2ysinx dy = 0 1+2ysinx dy = -cosx dx…

Q: iii- y +y tan .* sin 2x, y(0) = 1. (Bernoulli Equation) %3D

A:

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

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

Q: - ual2) V17 – cos(27at) (2 – 4t) sin(#) Given f(r) = edt, find the equation of the line tangent to…

A:

Q: Q3 Find dy/dx on the graph y sec/x+ y? = cos2x at point (1, 2).

A: We have to find dy/dx at (1,2).

Q: FIND Y(S) OF THE GIVEN EQUATION. y" + 4y = cos(t-3) +4t, y(3)=0 y' (3)=7

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Q: The integrating factor that can be used to turn the following non-exact equation into an exact…

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Q: 4. Solve dx - dy = 0 xy-1 xay

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Q: cos e de =_ %3D • 2 • -T • 6

A: “Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: The velocity of a particle moving along the x-axis is given by: v(t) = 1 cos(nt), t>0

A: Use the defination of velocity than solve the differential equation by separation of variables.

Q: i- y' + 2y 4 cos 2x. yT) = 3 (using Bernoulli Equation) %3D %3D

A:

Q: f(t) = e3t + cos 6t – e3t cos 6t ; L{f(t)} =? %3D -

A: given ft=e3t+cos6t-e3tcos6t

Q: Determine the form of a particular solution yp for y"+y cosx

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Q: +3x2, (V)² = sin³(cos³(*3**» dy b. Find dx %3D

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Q: Find the solution to the Bernoulli Equation. (3siny-5x) dx + 2x² cotydy=0

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Q: S2(cosx)(sin2x)dx %3D 3.

A: .................(1) take  put all values in equation 1

Q: cos(4x) dx - Find the Cauchy principle value (showing details): J (+5x2+4)

A: Given integral is, I=∫-∞∞cos4xdxx4+5x2+4 So, the function is, fz=cos4xdxx4+5x2+4 Now, consider the…

Q: i+ cż + x = cos t, e>0.

A:

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: 2 cosh V5t + t5 1 -2t sin 2t

A: Definition of Laplace transform :Let f(t) be a function Laplace transform of the function is…

Q: 6. J1-cos I COS T dx

A: Answer is mentioned below

Q: Let y = =tan(4x + 6). Find the differential dy when x = 5 and da Find the differential dy when x = 5…

A: A detailed solution is given below.

Q: 3.) Solve the equation using discontinuous function: y" + 9y = cos(2t) – U37(t)cos(2t) , y(0) = 0,…

A: We will find out the required solution.

Q: t/2 SL cosx/1+ cos²xdxdy is equal to 0, siny

A: Consider the iterated integral, ∫ab∫f1xf2xfx,ydydx In this iterated integral, the integration is…

Q: e-3t sin (4t) y (0) ==

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Q: Use the method of isoclines to draw several solution curves for the equation: dy/dx = x/y

A: We can use isocline lines to draw constant slopes along that line. Using some (at least four but six…

Q: dx -(I+ 2x tany) ay co

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Q: Find an equation such that y xe" cos(2x) is its solution.

A: To find an equation we derivative both side with respect to x.

Q: S-* cos(x²)dxdy = Q2): Show that 1-y2 %3D 6.

A: