Find the solution the initial value problem x' -13 X, %3D 1 -3 (1) x(0) cos(3 t) – 4 sin(3 t) x = e cos (3 t) – 2 sin(3 t)

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Q: sinx dy = 0 y cos xdx + 1+

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Q: Solve the differential equation 2 ď²y dy + 4y = cos(ln x)+x sin(ln x), r > 0, dr dr? by using the…

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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: Find all singular points for the differential equation (x+4 x)y" + sin(x) y' –x² y=0

A: Given differential equation is  x3+4xy''+sinxy'-x2y=0y''+sinxx3+4xy'=x2yx3+4x Let P=sinxx3+4x  ,…

Q: Solve the differential equation. y'+y tan x = cos x, - n/2 < x < r/2 A y = x sin x + c cos x, - 12…

A: Consider the given linear differential equation which is required to solve. Comparing the above…

Q: Q4// Solve the partial differential equation a²u ди cos*x given that = x when y=0 and u=3 when x=0?…

A: The given partial differential equation is ∂2u∂x∂y=cos4x Integrating on both sides with respect to y…

Q: Solve the differential equation. 7. (cosx cosy – cotx) dx – sinx siny dy = 0

A: This is a problem related to differential equation. Based on the general formula and concept we will…

Q: Find the solution of the Differential Equation: dx/dt=cos x cos^2 t

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Q: 2) Integrate: f (sin 13x - x + 5e +3 cos 3x +)dx 3) Solve the initial value problem : y 8. y(1) = 5.…

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Q: dy +(cos x)y = sin²(x) using first order linear differential equation. dx Solve (sin x) %3D

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Q: (1+x*)dy + x(1+ 4y²)dx =0

A: topic- differential equations

Q: Solve for the differential equations of  (e^x sin y - 2y sinx) + (e^x cosy + 2 cosx)y′ = 0

A: Given : (e^x sin y - 2y sinx) + (e^x cosy + 2 cosx)y′ = 0

Q: a. Verify that the function y = cos x - sinx + x² - 2 is a solution of the given differential…

A: As per the rules we are supposed to answer the first question and rest can be reposted.

Q: Find the solution of the differential equation tan x dx +tan y dy=0.

A: Here we have to find the solution of the differential equation  tanx dx + tany dy = 0.

Q: Find the particular solution to the differential equation: dy dx 3x2 cos? y. Solution passes through…

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Q: Solve the differential equation by variation of parameters. y"+y = n²(x) xx) = c₂cos(x) + csin(x) +…

A: The solution is given as

Q: xcosydy + sin2ydy – dx = 0

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Q: Solve the IVP of differential equation and write the interval / a) where the solution exist, b)…

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Q: Find the general solution of the differential equation. Use C, C1, C2,⋅ ⋅ ⋅to denote arbitrary…

A: Consider the given differential equation: y'x=4tan2x-3cosx Here, the objective is to find the…

Q: Find a solution for y in terms of x that both satisfies the differential equation and passes through…

A: We have to find the solution of differenrial equation

Q: The general solution of the differential equation by direct method: dy sec2 x dx 1+ 2 tanx y =…

A: According to the given information, it is required to find the general solution of the given…

Q: Solve the differential equation by variation of parameters. y" + y = sec (0) tan(0) y(0) = c₁cos (0)…

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Q: Solve the initial value problem for the differential equation: xy' = y + x2 sinx where y(n) = 0

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Q: xcosydy + sin2ydy – dx = 0

A: First arrange it in the bernouilli equation then find its integrating factor. Then  use the formula…

Q: dy cos(x). + y sin(x) = sin²(x) cos(x) y³ dx

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Q: The solution of variable separable differential equation -1+y* is %3D dx 1+x² a) tan y =tan x+c b)…

A: As per our guidelines I am solving one question. Please resubmit other question.  I am solving…

Q: Find the general solution of the differential equation 2e dy dr sin(x/2)cos'("/2)

A: For detailed solution of the problem see the next steps.

Q: (f) y' – 2y = 1 + 2x – sin(x)

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Q: Find the particular solution of the differential solution dy/dx=x^2(y+2) given that the point (0,5)…

A: Given,  The differential equation  dydx=x2y+2   Point 0, 5 lies on the graph of the solution  We…

Q: Find the general solution of the differential equation: (1+cos(I)y-(sin(x)y 2x y'+ sin(a) 1+co6(x),…

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Q: The solution of the differential equation using variable separable 4/1- y². O sin y = 4x +e O cos 'y…

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Q: dy/dx+(sinx/cosx)y=2cos^2sinx-1/cosx of first order linear differential equation y(pi/4) = 3√2 find…

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Q: Solve the differential equation y""+y" = 3x² + sin x - 2 cos x What is the particular solution?

A: We have to find the particular solution.

Q: ind solution of order differential equation  dy/dx=cos^2(x-y+1)

A: To the find solution of order differential equation :-

Q: Find the differential equation whose solution is                    y = A cos 8x + B sin 8x

A: We have to find the differential equation whose solution is  y = A cos 8x + B sin 8x  Here ,  2…

Q: (3tan x – 2cos y ) sec 2 xdx + tan x sin ydy = 0 %3D

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Q: y' + (2 tan x)y = cos³ x = COS" X

A: The correct answer is option (I) , i.e.  y = (cos²x)(c+sinx) The detailed solution is as follows…

Q: Solve differential equation (2y cos y - x sec y - x tany)dy = (1 + sin y) dx

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Q: Solve the differential equation cos(x + y) dx + (3y² + 2y + cos(x + y)) dy = 0. f (y). Express your…

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Q: Solve the initial value problem that consists of the differential equation x sin y dx + (x2 + 1) cos…

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Q: Solve the differential equation dy tan y x Cos x 3 dx

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Q: Solve the first order differential equation to find the particular solution. (cos x) + y sin x = 2x…

A: To solve the given differential equation.

Q: Solve the differential equation by variation of parameters. y" + y = sec (0) tan(0) y(0) = C₁cos (0)…

A: Sol:- While solving the question , initial θ is considered as 't' At the end , we will replace t…

Q: dy 47. = cos cos 2x, y(0) = 3 dx

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Q: 2x sin2(y) dx − (x2 + 12) cos(y) dy = 0 is given by  ln(x2 + 12) + csc(y) = C.   What is the…

A: bring every x terms one side and y terms another side.

Q: Find the particular solution of the differential equation (2xy - sin x)dx + (x² - cos y)dy = 0, when…

A: Exact differential equations

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

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Q: Solve the differential equation dy – y² sin(2x)sin²(x) = 0, y(0) = 1 %3D %3D - dx

A: Given that: dydx-y2sin(2x)sin2(x)=0, y(0)=1