1: Find the general solution of the following equations: I. dy_2r+2y-3 X-y-1

Q: Discuss the nature of the solutions of the equation 2x(1+x)y′′+(3+x)y′−xy=0 near the singular…

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Q: Solve the Sturm-Liouville problem 2. Q.7 x*y" + xy'+(16+1)y=0, y(1)=0, y(e" )=0

A: Sturm Liouville problem

Q: Find the singular solution to the Clairaut equation y = xy' + In(- 19 -y').

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Q: y(4) + 2y" = 2

A: Here we need to find the particular solution of given differential equation. The solution is…

Q: Solve the initial value problem: y'(x) = _Y(x) Vx-1 x> 1, y(2) = 1, %3| by separation of variables…

A: Hello. Since your question has multiple parts, we will solve the first parts for you. If you want…

Q: 3. Solve Bernoulli equation: xy' = y + y³

A: The differential equation is given as xy'=y+y3 It can be rewritten as…

Q: The general solution to y'' - xy' + y = 0 is given by:

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Q: find the general solution of the given equation. 3y'' - y' = 0

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Q: Give a particular solution for y"– 2y' + y = ; ex 1+x2

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Q: Solve the second-order equation y" + 2y' – 3y = 9x with initial condition y(0) = 0, y' (0) = 0.

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Q: Find the general Solution of DES: x yy'= x +3y

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Q: Find the solution of the initial value problem. 2y" - Зу' + у%3D0, у(0) %3D 2, y'(0) =

A: Here first we write an auxiliary equation of a given differential equation then  finding roots of…

Q: Solve the initial value problem. x2у" - 4хy' - бу%3D 0, у(1) %3D з, у'(1) %3D 4

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

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Q: Find the general solution to y" – xy' = 0. -

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Q: Find the complete solution of: y" + 4y' + 3y = e with y(0)=1 & y'(0)=0 4.

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Q: (a) Solve y" + xy + (2r – 1)y = 0, %3D near z = -1, if y(-1) = 2; y'(-1) = -2.

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Q: Solve the initial value problem y +i6Y = x, 1 -2 y(1) = 3 y(x) = (1/(x+6))*(In(x)-(6/x)+15)

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Q: 6. Find a general solution to the third order equation y" + y" + 3y – 5y = 0.

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Q: I Find a particular solution to y" + 4y' + 3y = 3te*. %3D Yp =

A: Solution:-

Q: Solve the initia value problem: dy 1 and y(1) = 1. dr

A: To solve the initial value problem dydx=x-1x    and    y1=1

Q: y" – 2y' + y = –3 – x + x²,

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Q: The general solution of the DE: -y = 1 is y= x(x + c)

A: given,1xy'-1x2y=1multiplying throughout by x we gety'-1xy=xnow, integrating factor μ(x) is given…

Q: 12. Find the general solution of x²dx + y(x – 1)dy = 0

A: This is a variable seperable DE.

Q: 3. Find the particular solution of the linear equation dy + -y = dr 1. if y(1) = 0.

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Q: 3. Solve y' = , with initial condition y(1) = 0. y2 – 1 x3

A: It is given that the differential equation dydx=y2-1x3. Using variable and separable method to…

Q: Solve the initival value problem: y = 2(5 + 9x)(1 + y²), y(0) : V3 1

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Q: 2. Obtain the general solution of the following equations: (i) x²uxx + 2xyuxy + y²uyy + xyux + y² uy…

A: If you want I solved other option please post it again

Q: Specifically a differential equations problem. Question in pic below.

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Q: Give a particular solution for y" – 2y' + y = ex 1+x2

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Q: Find two linearly independent solutions of y" + 3ry = 0 of the form Y1 = 1+ a3x³ + a6x® + · .. Y2 =…

A: We find two linearly independent solutions of the given differential equation  y"+3xy=0.......(1)

Q: Find the general solution of ди ди (y – z) + (x – z) ди + (2y – 2x) ду - az

A: The differential equation is given as (y-z)∂u∂x + (x-z)∂u∂y  + (2y-2x)∂u∂z = 0 We will solve it by…

Q: 4. Solve the IVP y' = 2x-3y +e¯* y'= 2x- 3 y +e * with y(0) = 1 y(0)= 1

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Q: 5. = y – xy³e-2x у —

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Q: If y and y, are solutions of a non-homogenous equation y" + ay + by =c then y,-Y2 is a solution of…

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Q: Obtain two linearly independent solutions valid near x = 0 x(1-x)y" - 3y' + 2y = 0

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Q: Solve initial problem xy’+6y=x^4,y(1)=2

A: Solve initial problem xy’+6y=x^4,y(1)=2

Q: Solve the given problem: y'' + 4y= 3sin2x

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Q: Q.7 Solve the Sturm-Liouville problem x² y" + xy'+(16+ 2) y=0, y(1)=0, y(e")=0 .......

A: Consider the Sturm-Liouville problem x^2y" + xy'+(16+lamda)y=0

Q: 1) Solve the initial value problem y-2ry = 2re Vỹ, y (0) = 1 and verify that the solution is true…

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Q: Obtain two linearly independent solutions valid near x = 0  x(1 - x)y" - 3y' + 2y = 0

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Q: The general solution of 5uxx – 6uxy +uyy = 0 -

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Q: Find the solution to the initial value problem. y'(x) = -y+ 2, y(0) = -2 %3D

A: Here, the given differntial equation is: y'(x)=-y+2...(1) with the initial value y(0)=-2

Q: Solve the Sturm-Liouville problem x2y + xy'+(2-1)y=0, y(1)=0, y(e)=0

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Q: Find the solution of the initial condition problem: ÿ +t°ÿ+3t?y = 0, ,y(0) = 1, ġ (0) = -1.

A: To solve the given differential equation with given initial conditions: y¨+t3y˙+3t2y=0;y0=0,y˙0=−1

Q: Find the particular solution of: y' – 4y = x²e* that satisfies y(0) = 2.

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Q: Find the general solution of y" + 2y=ex +2.

A: The Auxiliary equation is D2+2=0 solve for D Therefore  D=±-2=±2i Therefore the solution is…

Q: find the unique solution of the second-orderinitial value problem. 12y" + 5y' - 2y = 0, y(0) = 1,…

A: Given- 12y"+5y'-2y=0 and the boundary condition is y0=1 and y'0=-1. To find- The unique solution of…

Vertices Of An Ellipse

In the study of the conic section of the geometry, An ellipse is a plane curve surrounding two focal points, or foci where the set of all locus of points in the plane has their sum of the distances to the two foci is constant. On the ellipse curve, it is the intersection point of the main axis. In an ellipse graph, the center of the axis is the midpoint of the line segment connecting the foci. The major axis is the line section that runs through the ellipse's foci, while the minor axis runs through the middle and is perpendicular to the major axis.. The ellipse has two endpoints on the major axis which are known as the vertices (in plural), vertex in the singular. The equation of the major axis is 2a, the equation of the minor is 2b and the distance between the major axis and minor axis is 2c. The semi-major axis has a length of a and the semi-minor axis has a length of b. The ellipse's vertices are determined by the elliptical orbit's equation and graph.