1. Draw and obtain the differential equation of a circles having its center on the line x =y and each passing through the origin. 2. Obtain the particular solution A. yy' 2x(y + 1) B. (x? + 1) dy = (y² + 1) dx 3. Solve using homogeneous coefficient xyy' =2(y² + 2x²)

Q: 7. Consider the differential equation dy -t y° . dt (a) Solve the initial value problem with y(0) =…

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Q: Using the method of undetermined coefficient differential equation y" – 3y' + 2y = e* is: %3D

A: Introduction: According to Theorem B, a specific solution must be added to the general solution of…

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Q: 13 Find solution of non-homogeneous differential equation (D* +1)y = sin (3x)

A: Find complementary function and particular integral

Q: B: By using Homogenous method solve the first order differential equation (1 + e*%) dx - e²% (-1) dy…

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Q: Find the general solution of the differential equation y" y 42y = -122t+84t². - - NOTE: Use t as the…

A: Given: The differential equation y''-y'-42y=-122t+84t2 To find the general solution of the given…

Q: solve the first order of differential equation dy/dx = y2 -4 using seperable method

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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 3. y' -- %3D xy+x²y3

A: See the details solution in below

Q: Consider the differential equation ÿ + 4ỷ + 4y = u y(0) = ý(0) = 0 and u(t) is a unit step.…

A: Given differential equation is y¨+4y˙+4y=uy(0)=y˙(0)=0 where u(t) is a unit step function. Let the…

Q: Find a particular solution to the differential equation using the Method of Undetermined…

A: Consider the given differential equation,

Q: (2xy-tany)dx + (x² – xsec*y)dy = 0; y(1) = *

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Q: 4. Find a third-order linear homogeneous differential equation which has the function r(t) = 3e-t +…

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Q: 3. The Bernoulli's form of the differential equation x' ydx+(3x-y'dy=0 is

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Q: The Bernoulli's form of the differential equation x³ydx + (3x¹ − y³ )dy = 0 is

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Q: Use the method of variation of parameters to determine the general solution of the given…

A: Here given the differential equation as y4+2y''+y=3sin t or D4+2D2+1y=3 sin t

Q: [6] Find the solution of the first order ordinary differential equation (1– 3y2) dy – x sinx dx=0, y…

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Q: Find a general solution of the second-order nonhomogeneous differential equation y" - 2y' + y =…

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Q: Given (1 + y³)y' = x². Determine a region of the xy-plane for which the given differential equation…

A: y'=x21+y3

Q: 2. Solve the differential equation: (y² + xy°)dx + (5y² – xy+ y° sin y)dy = 0 by finding an…

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Q: 1. Draw and obtain the differential equation of a circles having its center on the line x =y and…

A: 1.

Q: Use the method of variation of parameters to determine the general solution of the given…

A: The differential equation given is y'''-y'=9t.  The auxiliary equation for the above differential…

Q: 4. Solve the differential equation 2x(2x – 1)- (x + 1)+y = 0 using the method of Frobenius. dx2…

A: 2x2x-1d2ydx2 +x+1dydx +y=0                       eq.(1) To solve by Frobenius series.

Q: Find the general solution to the non-homogeneous differential equation using the Method of…

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Q: Consider the solution to the differential equation y' with y(1) = 1. 3x (a) Apply Euler's method…

A: Given y'=4y3x with y1=1 Here, x0=1, y0=1 (a) We will find the value of y2 by Euler's method with a…

Q: 16. What is the particular solution of the linear differential equation y' +y = sec e", whose…

A: The solution is given as

Q: Find the solution of the first order differential equation with the given initial condition: y…

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Q: Let the following higher order differential equation y" – 2 y" – 3 y' = 3e5z (1). Determine the…

A: Consider the given information: y'''-2y''-3y'=3e5x To find the general solution by variation of…

Q: 3. The Bernoulli's form of the differential equation x' ydx+(3x - y³ dy=0 is

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Q: 2. What should be A for the exact differential equation of ry + A , 2Ay – 1 dr+ y? Moreover evaluate…

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Q: (2) Find the equilibrium solutions, classify the points and also plot the graph for the given…

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Q: 6. Find the general solution of the following differential equation using variation of parameters.…

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Q: 1) Find the general solution of the differential equation. y^(4)-y=4t+cos(t)

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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: Find the general solution of the non-homogeneous differential equation Y” –  2Y’  + Y  =  4 cos x

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Q: 2) find the complete solution of the differential equation x dy +Jx²-y*dx = ydt

A: given xdy+x2-y2dx=ydxxdy=(y-x2-y2)dxdydx=(y-x2-y2x)put…

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Q: Solve for the particular solution of the non-homogeneous differential equation. 1. y''+y=2x

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Q: Determine the particular solution of the given differential equation: y = 2(3x +y) – 1. when x-0.…

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Q: Use the method of variation of parameters to determine the general solution of the given…

A: The solution is given as

Q: Use the method of variation of parameters to determine the general solution of the given…

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

A: Since you have asked multiple questions in single request  so we  will be answering only first…

Q: Find the solution to the first order differential equation using any acceptable method.…

A: Given: The first order differential equation is (y2+1)dx = (ysec2x)dy.The initial condition is…

Q: The y(1) value of the y'= x + y differential equation that satisfies the condition y0)=1 by taking…

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Q: Consider the differential equation, y'+ ty = t , with the initial condition that y(1) = 4.  Use…

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Q: For the differential equation y' = 2y - x, draw line segments representing the slope field at the…

A: Given that, y' = 2y - x dy/dx = 2y - x At the point (1, 2) we get: dy/dx = 2(2) - 1 dy/dx = 4 - 1…

Q: (20) Determine the complete solution of the differential equation y" + 4y = 2cos2x subject to…

A: Solution: The objective is to find the general solution of the given differential equation