1. Use the VP method to find the general solution of the DE y" + 6y' +9y= 3z 23

Q: Find the general solution to the equation xdx + -dy= 3dy O x=/2y+ Cy-2 O xy= 2y + C O y = 2x3 + C…

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Q: 6. Find the general solution of X Ury -Y Uyy = Uy %3D by using the change of variables: v = x, w =…

A: Given: The partial differential equation, xuxy-yuyy=uy   To find: The general solution of the given…

Q: 6. Find the particular solution of ydx – 4xdy = y6dy; where x = 4 and y = 1.

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Q: 7. Find the general solution, by the method of undetermined coefficients. y" + 4y' + 4y= 10e-2 -…

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Q: 2. Find general solution of the DE y" + 3y" + 3/ + y = 0

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Q: Find particular Solution of y-2y'ty =x-6x +2xe a 2.

A: Solution.  Given the differential equation                   y''-2y'+y=x2-6x+2x2 ex…

Q: f(x) = -12-21x + 18x^2 - 2.75x^3 what method will give a root of the function equal to - 0.287425 in…

A: We will use a numerical method to determine what will be the value of root of the given function in…

Q: y-3y" + y' + 5y =

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Q: 6. Find the general solution to y" – 6y" = 3 – 6e2z

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Q: Determine the particular solution, yp of y" + 2y' + 5y = –2cos(2x). оа. Ур — — Аcos(2a) O b. Yp =…

A: Particular solution

Q: (2) z?y" – ry + y = 4x lnx

A: Given DE is x2y''-xy'+y=4xln(x)......(1) We solve this DE.

Q: 2. x + y – z = 2   2x + 2y - 2z = ­6  5x + y – 3z = 8

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Q: Let (x, Y,) be the solution of the following equations (2x)" = (3y)m3 3Inx = 2lny In 2 %3| %3D Then…

A: Introduction :

Q: -) Find the gereral solution uf y-3y'+2y= 4k2xe"

A: Given,          y''-3y'+2y = 4x2+2xex               (1)

Q: Find the general solution to y = c₁e¹¹ + c₂e(8-√³)² + cze(8+√7)₁ Oy=c₁e¹¹ + c₂e³ + c3e-81 Ⓒy=c₁e¹ +…

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Q: Show that y %3D Cіx-1 + С2х + Cзlnx + 4x2 is a solution to x3y" + 2х?у" — ху' + у %3D 12х?.

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Q: Verify that yp, =3e²x and yp₂ = x² + 3x are, respectively, particular solutions of y" - 6y' + 5y =…

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Q: Find a particular solution to Ур y" + 4y + 4y = -9e-2t t² + 1

A: The  given  equation  is (y''+4y'+4y)=-9e-2tt2+1………(1)Here, y'=dydt ,y''=d2ydt2 Thus,  the  given…

Q: Find the general Solution of 2y +4y=0 oy 25y= o づV

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Q: the general solution of yv1+x²dx + x/1+ y?dy = 0 using variable separable method. 3. Obtain X-

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Q: 4y" + 12y' + 9y = 0.

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Q: Find a particular solution to y" + 6/ + 9y = 3.5e 3. Yp =

A: Given thay  y"+6y'+9y=3.5e^(-3t) To fin the particular solution

Q: Obtain the general solution of 25y" + 30y' + 9y = 0. %3D y = C1xe" + C2x²e Y = C1e¯5ª + C2xe¯" -3x O…

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Q: Find a particular solution to Ур = y" + 8y + 16y -10e-4t t² + 1

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Q: 5. Find the general solution of (D³-D)y=4e*+3ex. Ans. y=2xe*+(1/2)e2+c1+c2e*+c3e*

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Q: nd a particular solution to = y" + 8y + 16y= = -15.5e-4t t² + 1

A: Particular integration by shortcut method

Q: Find the general solution Y" + 4y² + 2y = ex

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Q: 1. V2 are two independent solutions of y" + p(t)y' + q(t)y= 0 then ect one: a. V1 b. C. W(y1.V2) d.…

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Q: The equation, d(t) = 255t + 5654 represents the tuition, d dollars, at a college for the year Find…

A: I have explained everything with in the solution .please go through that.