Determine the solution of the following equations: 1. (x*D² + 2xD- 2)y = 4 + x² 2. (x'D³ +3X°D² +xD - 8)y = 7x– 4

Q: Solve Cauchy-Euler equation. a2y"-2y 2x %3D

A: (1) The equation is, x2y''-2y=2x Take y=xm Then take the derivative, y'=mxm-1 Take the derivative…

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Q: Find the general solution of the equation d2y/dx2 - 2dy/dx +4y =2ex sin2(x/2)

A: Given the given differential equation is d2ydx2-2dydx+4y=2exsin2x2

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A: This question is related to differential equations, We will solve it using given information.

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Q: Find the solution of the equation 3U,-5U, =0 satisfying the condition U(0, y) = sin y

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Q: Employ Picard's method to obtain y (0-1) of the equation y,=0 when x =0. :=x² +y}, given that %3D

A: Given IVP is dydx=x2+y2, y0=0 when x0=0 Let f(x,y)=x2+y2 , y0=0 when x0=0. Formula for Picard…

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Q: 4. (D² + 2D + 5)y = 4e-*cos²x

A: Given differential equation is: d2ydx2+2dydx+5y=4e-xcos2x Auxiliary equation corresponding to given…

Q: Solve the problem. 5) The position of a body moving on a coordinate line is given bys = t2 - 6t + 2,…

A: The position function of the particle is The velocity function is evaluated as Now, we will find…

Q: Find the general solution of the equation d2y/dx2 - 2dy/dx +4y =2e sin2(x/2)

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Q: Solve 1 . Find a particular solution to a' = x – y + e', y = -4x + y +t using undetermined…

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Q: Solve the stated IVP using the method of undetermined coefficients.   y’’ + 3y’ = 3 sin 2t, y(0) =…

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Q: dy 2y ! = -x² y² sec²x %3D dx +

A: Using solution of Bernoulli Differential equation.

Q: a) Find the general solution of the equation dªy dy dx² 4- x2 + 3e* - dr4 by using the method of…

A: As you have posted multiple parts,but they are independent so according to our guidelines we will…

Q: Find the general solution for the homogenous equation of y′′ − y′ − y = 0.

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Q: - Find the solution of the equation 3U, -5U, = 0 satisfying the condition U(0, y) = sin y

A: We have to find the solution to the given equation.

Q: y" + 2y' = 121?

A: To find the general solution of a given non homogeneous differential equation first we will find…

Q: Solve (D2 – 2)y =0 O a. y = cqevZx + c2e¬vZx O b.y= "(c,cos/2x+ c,sin/2x) O c.y = cqevZx+czxe¬VZx O…

A: The equation D2-2y=0 represent y''-2y=0 . Consider the solution of the differential equation is in…

Q: Find the solution. (Dª+2D3 + 10D2)y =0. @y = c,e-+czxe¯+e"(e,cos3r +c,sin3x) y = (c,+c,)x+e*(c,cos3x…

A: To solve the given Differential equation.

Q: Solve: (2x + 3y – 5)dx + (3x – y – 2)dy = 0 . Show solution for determining the coordinates of the…

A: Find your answer below

Q: 2x y" + 4y' + 5y = cosx

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Q: Find the general solution of the equation xy' = ky that is valid for x > 0.

A: We have to find y(x) for this equation which is valid for x>0. We use integration to solve this…

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Q: Find the general solution and particular solution of this equation. (Non-anonymous question) xydx +…

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Q: 1. Solve the linear equation y' +y = 5 sin 2t.

A: Given that  y'+y=5sin(2t) To find the general solution of the differential equation

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

Q: Match the equation to the graph. y 2 sin 30 - 1 %3D Sn / 3n 7n 21 4.

A: y=2sin3θ-1Use the form  a sin ( b x − c ) + d  to find the variables used to find the amplitude,…

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Q: The equation y = xy can be classified as FOLDE and Bernoulli’s equation. True False

A: Given that, Differential equation is following, dydx+4x2y=xy We have to find that this D.E can be…

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

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Q: The direction field for = 2x + y is shown in Figure 1.12 1) Sketch the solution of the curve that…

A: Equations are given below

Q: A particular solution of the equation y(4) + 2y" + y = 9 cos(t) + 2et – 5t is of the form

A: See the detailed solution below.

Q: Obtain the roots and the factored operator form linear differentia equations y = x e* sin 2x + 3 e*…

A: First we find the annihilates polynomial of given function then find auxiliary equation and…

Q: The equation (tan²x+3y²)sec²xdx + (3tan²x + y²)dy=0 can be solved by

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Q: he equation ay"+ by' + cy = 0 has a unique solution satisfying y(0) = 1 and y'(1) = 2.

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Q: Given, 1 y" +-y' + y = 0 x2 Write 2 linearly independent solutions (in the form of Bessels'…

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Q: Solve the nonhomogeneous equation using the method of undetermined coefficients: y +4y=x-2 cos 2x,…

A: The solution is given as

Q: Solve of the following equation 4 y' +y = x'y? Given by x3 In x – c -x3 In x + c O Option 1 O Option…

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

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Q: 42. y" + 4y = sec² 2x

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Q: Find the general solution of each nonhomogeneous equation. 1. y" + 4y= 8

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

Q: Find the equation of a line parallel to x = -8+ 2y that passes through the point (8, –2). Oy = -x –…

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Q: Find the general solution of the equation y" − 4y' + 3y = sin(x)e²x -

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Q: Solve the bernoulli's equation x(6x^2−y−1)dy +2ydx =0.

A: The given Bernoulli’s equation can be written as:

Q: 7. A swimmer orients herself perpendicular to the parallel banks of a river. If the swimmer's…

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