Find the differential equation of a family of circles, each having its center on the line y = z and each passing through the origin. Oy=Y¹-2-2² y²-2ry-2² O y'= y²-4ay-22¹ +4ry-20¹ y² + 2y+z² ²+2y+z¹ O y = Oy=1¹-22-22 y² + 2ry-z² Oy y²+2y+z² y²+2y+z² ¹-2ay-2¹ Oy v²+2ry-z² ter on the line y can =

Q: Which of the following is the general form of a homogenous equation? A a,(x)y"+a+ ...,(x)y"=0 (x)…

A:

Q: general form of a homogenous equation? )y" -l+ ... +a,(x)y'+a,(x)y=f (x)…

A: We have to choose the correct answer from the given options according to the given information

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A: Use the definition

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A: Given

Q: 2. a) Find the general solution of (z²-2yz-y²)p+(xy+xz)q=xy-xz, b) which passes through the curve…

A:

Q: 2. Consider Pell's equation associated to n = 2: x²2y² = = 1. One of the solutions is N(1, 0) (a)…

A: “Since you have posted a question with multiple sub parts, we will provide the solution only to the…

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

A: Solution ) we have option 3rd  y"+ 4y = 0 Auxilliary equation  m2 + 4 = 0 m2 = -4 m = √( -4 )  m =…

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A: According to questionWe have to draw the phase plane for the given points.

Q: Q.No.3: a) Solve Cauchy-Euler equation d'y 3x3 dx3 d²y dx2 dy + 9x? + 6х— — бу %3 1+x3 dx

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Q: Determine the corresponding differential equation for a family of parabolas with focus and vertex on…

A:

Q: Classify each of the equations above as autonomous, separable, linear, homogeneous, exact,…

A: I am solving questions ( B I and J ) as per the guidelines we can solve max 3 sub part of a question…

Q: rewrite the following second order linear equation into of two equations. y'' + 5y' - 6y = 0

A: Given y''+5y'-6y=0

Q: Q.No.3: a) Solve Cauchy-Euler equation d'y 3x3 dx3 d'y + 9x2 + 6x dx2 dy 6y = 1+ x3 dx -

A:

Q: Solve 1- y"- 6y' + 9y 4e Ans. y Ce +c,xex+2x2er

A: Note: Since you have posted multiple independent questions, we will be solving only the first one…

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A:

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A:

Q: Obtain the differential equation of the families of circles with center on the line x-y = 0 and…

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Q: hird-order Euler equation is one of the form ax y"" + bxʻy" + cxy' + ky = 0, where a, b, c, and k…

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Q: Which of the following equations is NOT an exact equation? dy=0 B (xy - cos x)dx + (x² – 1)dy=0 (2x…

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Q: x² – 9y2 : -9y2 = 13 x² + y² = 53 %3D

A: Given,

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A: Given center of the circle is on the x axis let center is at x= a so coordinate of center = ( a , 0…

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A:

Q: dy 1. dx = 6y d y 36у dx2 dy = -36y dx2 2. 3.

A: We are entitled to solve only one question at a time and up to 3 sub-parts only. So, we will answer…

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A: