Determine the types of the following equations. their general solutions And find zy 4 y²dxx +2 (1-1²) sxy -tyy - 1+y= (2Ux-ly) 20₁ туг XEIR, y ₂o.

Q: Solve the following Bernoulli equations: (a) dy dr. + xy = zy³,

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Q: C.1. Give a real general solution to the equation u'''' - 5u''' -6u'' = 0 :

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Q: 1. Eliminate the arbitrary constants on the given equation: y = Aeª + Bxe*

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Q: Find all solutions of the form y = erx for the equation y''−y'−2y = 0. Then write the most general…

A: This is a second order differential equation. The solution of a second order differential equation…

Q: Solve the exact equation (+22) de +(+2y) dy = 0. The solutions are of the form F(z,y)=c, where…

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Q: Find the general solution of the following equations in the standard form (ax + by = c). 1. (2x -…

A: We need to solve D.E.

Q: x² + 4y² = C(x+y)

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Q: The Cauchy-Euler equation can be reduced to an equation with constant coefficients by means of the…

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Q: Find the change of variable x = Py that transforms the quadratic form x¹ Ax into y¹ Dy as shown. -…

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Q: Solve the given D.E. by the method of undetermined coefficients. (Find y = ye+ yp) y" - 7y +12y =…

A: Introduction: Before proceeding any further let’s again note that we started off the solution above…

Q: Convert the given equation into the form of a Sturm-Liouville equation. y" +7y' + ay = 0 Write the…

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Q: Determine if y = ex is a solution to y′′′- 12y′′ + 48y′- 64y=0

A: y'= ex  y"= ex  y'"= ex

Q: canonical form

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Q: we will use the method of separation of variables and Fourier series to derive a solution formula…

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Q: y' = x – 2ycot(2x) %3D

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Q: Find the general solution using substitution of each of the following DE: 1.) (2x + y + 6) dx + (2x…

A: As per our guidelines, we are supposed to solve only first question. Kindly repost other question as…

Q: Find the general solution to the equation y4) – 6y" + 9y" = 0. NOTE: Use c1, c2, C3, and c, as…

A: We can rewrite the given equation as y''(y''-6y'+9y)=0 Put y = erx then y' = rerx and y'' = r2erx

Q: 1. х2у" — 20у%3D 0

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Q: Solve the following DE: x³ydx + (3x4-y³) dy = 0 O 15x5y 10 2y ¹2+ C ○ 4x6y 10 = 3y ¹2+ C 12 O 15x4y…

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Q: Find two solutions to 2y′′+ 5y′+ 2y= 0

A: for the homogeneous system, the auxiliary equation is given by

Q: Find the general solution to the equation y(4) – 16y" + 64y" = 0. NOTE: Use С), С9, Сз, апd сд as…

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Q: Solve for the Linear Equations y′=x−2y

A: y'=x-2y⇒y'+2y=x Now comparing with y'+Py=Q, we get P=2  &  Q=x Now integrating factor is,…

Q: Solve the given equation.. (3x² + y)dx + (x²y-x)dy=0 a. b. C. ²- +3x=C x²y²+x²y + x4 = C x² - + x =…

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Q: Find the value of A so that y=Ae2t will  satisfy the equation y′′ − 2y′ − 3y= e2t

A: we have to find the value of A so that y=Ae2t will satisfy the equation y''-2y'-3y=e2t as y=Ae2t…

Q: Determine a suitable form for Y(t) if the method of undetermined coefficients is to be used. -t y(4)…

A: To determine the suitable form for Y(t) if the method of undetermined coefficients is to be used.…

Q: Find the general solution for the equation dy a² + (xy)- 2.ry + y? dr

A: The differential equation is given as x2+(xy)dydx = 2xy+y2xy dydx = 2xy+y2-x2dydx = 2xy+y2-x2xy…