3. (a). Show that the differential equation below is exact. Hence, determine its implicit solution. (3x° cos y-x)dx = (x sin y)dy, y(1)=0 (b). Determine the general solution of the following Bernoulli differential equation dy y -ey*. dx 3x

Q: 31-Which of the following is the y(0.5) value of the y'= x - y differential equation satisfying the…

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Q: -(* +2) Solve for y = y (a) in the differential equation dy if y (0) = 1. No need to isolate y. %3D…

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Q: 2xydx = (x2 + y²)dy ;y(0) = -1 Ans: y(y + 1) = x²

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Q: For the second-order differential equation y" + 9y = 6 cos x: a. Show that y = cos x is a solution.…

A: The given differential equation is: y''+9y=6 cos x

Q: The growth of a certain type of weed satisfies a differential equation of the following form, where…

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Q: 3. Find the general solution of this separable differential equation. dy y cos x dx sin x + 2

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Q: Determine the values of r for which the differential equation y + 2y = 0 has solutions of the form y…

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Q: If a nonhomogeneous linear differential equation has g (a) = sin 5a, what is the form of its…

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Q: 1. Given the following differential equations (DE): A. e*y' = x – 2y в. у' — еу 3 sin x Identify if…

A: according to our guidelines we can answer only three subparts, or first question and rest can be…

Q: Solve the differential equation y" + y' +y = sin(2t) subjected to the conditions y(0) = -2/13 and…

A: solving by Laplace transformationgiveny''+y'+y=sin2t and y(0)=-213 ,y'(0)=713taking laplace on both…

Q: 1. Given the differential equation: y" = sin(5x). Determine its general solution. A. 150y = cos(5x)…

A: Given differntial equation          y'''=sin 5xthen we have to find it's general solution…

Q: 1. Consider the equation (x + 2e + 2y) dx + (2x + cos y) dy = 0. (a) Show that the equation is…

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Q: # 2.) Given the differential equation, y'=4cosx-3y, y(0)=1, a.) Use Euler's Improved Method to…

A: Given the differential equation, y'=4cosx-3y With the initial condition y(0)=1 Here,…

Q: 9. For the differential equation condition y(0) = 1. dy -- y = ey², solve for y = f(x) given the…

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Q: 4. Find the differential equation of the family circles entered at (h, k) passing through the origin…

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Q: 1. Consider the differential equation: dy = = 2y - cos (3t) dt a. Find the homogeneous and…

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Q: 1. A solution for the differential equation is y = e"x A, sin (vx) + A, cos (vx), where m and n are…

A: Let's find.

Q: 2) Show that y = A cos x + Bsin x, where A and B are constants, is a general solution of the…

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Q: 11. Solve the second-order differential equation y" – y' – 2y = 20 cos x using the method of…

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Q: 1 Obtain the particular solution for the following differential equation if y(n) = 1 (3x? + ycosx)dx…

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Q: 6. a. Solve the differential equation below under the following initial conditions: y (0.5), y (1.0)…

A: Since you have posted a multiple question according to guildlines I will solve first question(a) for…

Q: 1. A solution for the differential equation is y = e"* A, sin (vx) + A2 cos (vx) , where m and n are…

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Q: (b) Consider the differential equation ydx + x(lnx-lny - 1)dy = 0. Hence, or otherwise, use an…

A: Let us consider a differential equation of the form Mdx+Ndy=0 To equation is exact if ∂M∂y=∂N∂x then…

Q: 4. (а) Find the general (implicit) solution to this differential equation. dy x – 5 (x – 1) dx y²(x…

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Q: Given the Differential Equation as 2xy2+4=2(3-x2y)dy/dx. A. Prove or disprove if the given…

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Q: B: By using Homogenous method solve the first order differential equation (1+ e») dx - ely (G-1) dy…

A: Let's find.

Q: If the function y = A sin z + B cos a satisfies the differential equation y" + y – 2y = sin z for…

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Q: The particular solution of the following nonhomogeneous differential equation y" - 2y' +y = x? + e*…

A: To find  The particular solutions of the given differential equations

Q: x2+1 y'= Ans: y = + x + In(x – 1)² +c = -X - X-1

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Q: 7. Choose the appropriate table for the differential equation X y ଶ୪ X y dx X Y -201 -4 1 2 2 -1 -1…

A: The solution is given below

Q: The given differential equation xyey + y*) dx – x²e)dy = 0, where y is not equal to 0 is best solved…

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Q: 3. (a) ! Show that the differential equation (r2-y2)dx-2rydy 0 is exact. (b) . 1 Find the general…

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Q: The Differential Equation 2y"" + 3y" – 3y' – 2y = e-t; where: y(0) y'(0) = y"(0) = 0 has a solution…

A: According to question, Given differential equation,2y''' + 3y'' -3 y' - 2y = e-t,y0 =y'0 =y''0 =0

Q: Find the value of k so that the given differential equation is exact. (7xy³ + cos(y)) dx + (2kx²y² -…

A: Given

Q: 5.- Use the method of undetermined coefficients to find a particular solution, Y, , for the given…

A: Take up in perfect form and put on the given differential equation

Q: 1. Find a homogeneous linear differential equation with constant coefficients whose general solution…

A: y=c1cosx+c2sinx+c3cos2x+c4sin2x For c1 and c2 α=0, β=1 α±βi0±1i0±i m-im+i=0m2+i2=0m2-1=0

Q: 1. Consider the following first-order ordinary differential equation 2,2 2x²y cos x dy + (2xy² cos x…

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Q: Solve for the particular solution of the differential equation 2xy = x² + y² with the given…

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Q: 7. Find a linear differential equation with constant coefficients Ly = 0 such that y(x) = cos(x) +…

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Q: 2) Show that y = A cos x + Bsin x, where A and B are constants, is a general solution of the…

A: Solved below

Q: Determine the values of r for which the differential equation y' +9y = 0 has solutions of the form y…

A: Given differential equation.

Q: Find the value of y for the given differential equation if the value of the arbitrary constants is…

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Q: Q-2) [CLO1(PLO1)] Solve the given differential equation subject to the indicated initial condition a…

A: 2) Given differential equation is  α +11 + y2 + cosx - 2xydy - yy + sinxdx = 0,   y(0) = -1

Q: 2) Show that y = A cos x + Bsin x, where A and B are constants, is a general solution of the…

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Q: 3. Given the DE with the form y' + yP(x) = (y^n)Q(x), where n is any real number. If n = 1, the…

A: I have show that for , n=1 given differential equation becomes variable seperable differential…

Q: The solution of the following separable differential equation x²y-y ア=リーン y' with y(3) = -1 is y+1…

A: Given,          y'=x2y-yy+1 with y3=-1

Q: 2. Determine the general solution of the given Differential Equation (x2 – xy + y?)dx – xydy = 0 - -

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Q: 1. a) A non-linear ordinary differential equation is given as: dy (cos* x) + y (sin x) (cos³ x) – y³…

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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.