b) y"+ 4 y = cos (t), y(0) = y'(0) = 0

Q: 7- cos y dx + (x siny - cos²y)dy = 0

A: Note: as per guidelines we support one question in one request . kindly repost next question in next…

Q: SOLVE FOR EXACT DE DIFFERENTIAL EQUATION 3. (x + 3)cos ydx - [siny In(5x + 15) - y] dy = 0

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Q: Find the differential equation of (y cos x + 2xe^y )dx + (sin x + x²e^y) dy =0

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Q: Find the particular solution for: y' sin(2y) - cosx = 0, x =when y = 0 %3D 2

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Q: Show that y = sin−1 x satisfies the differential equation y = sec ywith initial condition y(0) = 0.

A: The given differential equation is y' =  sec y,  with initial conditions y(0) = 0.We want to show…

Q: Solve the first order differential equation dy ycos' x 1+ sin x dx

A: The given equation is first order, linear differential equation.

Q: Verify that the function y = x sin(x) + x cos(x) is a solution to the differential equation: y" + y…

A: 1 have verified the differential equation by finding each derivatives

Q: y(cos 2x)e*y – 2(sin 2x)e*y + 2x + [x(cos 2x)e*y – 3] = 0 %3D dx

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Q: What is the general solution to the differential equation (3 tan x – 2 cos y) sec?x dx + tan x sin y…

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Q: (2y-1 + cos 3z) 분. 4x3 + 3y sin 3x = 0 (1)

A: We know that if - M(dy/dx)+N=0 Then M(dy/dx)= -N Therefore- dy/dx= -(N/M)

Q: 3) y sin-ly² dy

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Q: 23 Find dy/dx on the graph y3 sec/x2 + y2 = cos2x at point (1, 2).

A: Use product and chain ruleof differentiation at given value

Q: 5- = cos nx dx= [cos nx cos nx dx 0.

A: We have to solve given problem:

Q: Verify that y=sinx is a solution to dx dy 2cos x-sin x+y and solve the 2 cosx differential equation…

A: Given Information :  Differential equation : dydx = 2cos2x - sin2x + y22 cosx  y1 = sinx y(0) = -1

Q: cos 2x dx (b) 4 cos t dt 0 2

A: Since you have posted multiple questions, we will solve only first question for you. To getremaining…

Q: Form the differential equation whose primitive is given by y= ex(a cos⁡x + b sin⁡x),  a, b, being…

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Q: 3. Find d²y/dx² of y= x cos (5x) – sin² x/ |

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Q: z = sin(6x) sin(5y) az az dy II

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Q: 11) (3ycos(3x)dx– sin(3x)dy)/ y = 0 12) sin(ß y)dx =-ß cos(B y)dy

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Q: Determine the general solution and the particular curve that goes through point (0,0) of the e* cos…

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Q: 2. [ * xkbr cos*x- sin 3(sin y- cos y)° dv 10. cos y

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Q: dy Cos(3x) + (In x)

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Q: Show that cos x is the integrating factor of the linear differential equation dy/dx= sec x+y tan x

A: Integrating factors are useful for solving ordinary differential equation  that can be expressed in…

Q: 4 sin (2x) dx cos (2x)t4

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Q: (cos 2y – 3x²y²)dx + (cos 2y – 2x sin 2y – 2x³y)dy = 0

A: We will find out the required solution.

Q: At any particular time, the rate of change at which the vertical position of an object moving in…

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Q: y + sinx cos2(xy) cos (xy) Ex. 13. Solve dx + %3D .cos?(xy) + siny ) dy = 0. CS Scanned with…

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Q: 1. S e sin 4x cos 4x dx 2. S dx Je-2x dx e 2x

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Q: 2. sin3x dx + 2y cos 3x dy = 0

A: Given equation - sin(3x)dx+2ycos33xdy = 02ycos33xdy =-sin3xdxydy =-sin3x2cos33xdx             Taking…

Q: Solve for the DE: (y²-1)dx + (2xy- Siny) dy =0 When x= -1 ; y= 0

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Q: The standard form of the differential equation cosx y' + cosx y = x sin x is: None of the above O…

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Q: 1- S7 cos(y)eSin(y)+9X dydx

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Q: dy Show that given differential equation da y cos z + sin y + y sin a + r cos y +x 0 is Exact and…

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Q: Find the curve y that satisfies the differential equation y' sin r and passes through the point (T,…

A: Integrating the equation

Q: 4. Form the first-order differential equation of y = e(sin y + r) %3D

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Q: At any particular time, the rate of change at which the vertical position of an object moving in…

A: A  detailed solution is given below

Q: Show that y is a solution of differential equation = 1-. dy %3D dx

A: y'(x)=1-yx We can simplify it as: dydx+yx=1First-order linear ordinary differential equation.…

Q: ( cos nx dx= [cos %3D nx cos nx dx 0. %D

A: We have to find the integral of cos2nx dx from 0 to 2pi.

Q: 4. STT- COs y dy -COS

A: The objective of the question is evaluate the indefinite integral.

Q: 1I) (3y cos(3x)dx-sin(3x)dy)/ y 0

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

Q: (y2 cos cos x – sin x)dx + (2y sin x + 2)dy = 0 -

A: The given differential equation is first-order non-linear ordinary differential equation:   First we…

Q: What is the general solution to the differential equation sin y (x + sin y)dx + 2x² cos y dy = 0 ?

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Q: What is the general solution to the differential equation (tan x)dy – (4y In y – y tan³x)sec²x dx =…

A: Given differential equation:(tanx)dy-(4ylny-ytan3x)sec2xdx=0To find: General solution of the…

Q: HW 0If y=tanx show that- yl" =-2 Siny coży

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Q: 2-€2x y") edxtcuxe yd-siny)lye.co

A: A differential equation of type   P(x,y)dx+Q(x,y)dy=0   is called an exact differential…

Q: The linear differential equation y' - cotx + 3y csc x = 0 has the integrating factor tan A tan () B…

A: The objective is to find the integrating factor of given equation: y'-cotx+3ycscx=0

Q: d'y dy dx² dx 21 29 - -6y=6e¹ cos x; when x=0, 20 dy dx =-629 y = 2e-3x - 2e²x 3e-* 29 (3 sin x - 7…

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Q: 2 sin x Show that y is the solution of the differential equation xy'+y=2 cos x.

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Q: 2. sin3x dx + 2y cos³3x dy = 0

A: Given- sin3xdx+2ycos33xdy=0 To Solve- The above differential equation.

Q: What is the general solution to the differential equation (tan x)dy – (4y In y – y tan³x)sec²x dx =…

A: We will convert given differential equation into linear differential equation by appropriate…

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.