Find the general equation of the following DE: 4. (D3 − D2 + D − 1)y = 4sinx

Q: Q3/ Solve the following equations: 1- х(2у — 3)dx + (x2 + 1)dy %3D0 dy 2- dx 4y x (у-3) 3. y' = 2xy…

A: Note that there are so many ways to write the final answer of the differential equation.

Q: nd the general Solution of the tfferential equation. (x+2y-1)dx+(3x (3x+by)dy = C

A: The differential equation is given as , x+2y-1dx+3x+6ydy=0. Simplify the differential equation,…

Q: Solve the D. E. to the I. V.P. (1 +x² + y² + x?y²)y' = y², 2. y(1) = 1

A: The solution is given as

Q: d²y Show that y = sin(2t) satisfies . + 4y = 0 dx²

A: 1) To prove the given equation 2) To find the value of w

Q: Find the solution of the D.E. below: 2(2x + y?)dx - xydy = 0 A x4 = 4c (x2+y?) B x4 = c (4x2– y?) x4…

A: Simplify the given differentiatial equation to obtain the expression of dydx.…

Q: Find the general solution to y"(t) = t1² – 3t* + e' – nsin (at). Show all steps

A: y"(t)=t12-3t4+et-πsin(πt)d2ytdt2=t12-3t4+et-πsin(πt)

Q: Use the method of reduction of order to find a second solution t t'y'' + 4ty' - 4y = 0, t > 0 |…

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Q: C. Given :v = (3t - x)e-2 , 1. Find at

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Q: Q.1 Put the D.E ey"+2xy' + ây = 0, in self-adjoin form .

A: Given the differential equation e-xy"+2xy'+λy=0 we have to put the given differential equation in…

Q: al equation - y² , y(1) = 2 is hod with step siz nd off to 2 place

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Q: • Find a general solution for the following by method of undetermined coefficient. a) y" + 4y = x?…

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Q: Find the general solution of (D4+ 50D²+625) y=0_ A y=c,cos5x +c,sin5x ® y=c,e*+c,x* +cze-5«.…

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Q: For y=x²-9x+8, find dy, given x = 1 and Ax = -0.1. dy = (Simplify your answer.) 5 2d

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Q: For y = x° - 2x + 8, find dy, given x= 4 and Ax = - 0.2. 3 dy = (Simplify your answer.) %3D

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Q: e-SP(x) dx x²(x) as instructed, to find a second solution y₂(x). 6y"+y¹ - y = 0; Y₁ = ex/³ Y₂ 11 Y₂…

A: Given DE is  6y"+y'-y=0 .......(1) Also given y1=ex/3. We find y2(x).

Q: for the exact equation of the form M(x,y)dx + N(x,v)dy = 0 Select one: O a. My- Nx b. NOTA C. My- Ny

A: Consider the differential equation of the form  Mdx + Ndy = 0

Q: The sales of shirts and ties at a store are related by the equation 0.6x + 3xy + 8.3y = 78659.1,…

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Q: Find the solution for t> 0. Note that you can assume yı(t) = t". t'y" – 3ty' – 12y = 0

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Q: F. Solve the following by Substitution Method. dy = (-5x + y)² – 4 dx 2.

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Q: y? x² 4 Find dV , where E is the solid y2 x2 + 4 z2 - <1. 9 + +

A: First we have Choose suitable parameters.

Q: For y=x -9x+7, find dy, given x= 5 and Ax= -0,2, dy (Simplify your answer.) dy%3D

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Q: Obtain the particular solution 1. (D³ +6D² + 12D + 8)y=0 when x = 0, y = 1, y'= -2, y" = 2 2. y" +…

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Q: I. Obtain the general solution of the following: a) (D2 + 3D + 2)y = 1 + 3x + x2 b.) (D2 − 6D +…

A: Use rules of differential equations

Q: Obtain the general solution.  1. (D4 + 3D3 + 2D2) y=0  when x=0, y=0, y'=4, y"=-6, y'''=14 2. (D3…

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Q: Solve the given DE. (D³ + D² + D+ 1) y = 0 ; y (0) = 2, y' (0) = 2, y" (0) = -4

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Q: 1. Obtain the general solution unless otherwise instructed d²y 1. y = 10sin²x dx2 %3D - SUMMARY OF…

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Q: 4y"-y=e^x/2+6 consider the following DE to be solved by variation of parameters

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Q: dy Find the general solution for: -6y dx Select one: O y=C.e¯z О у y = C. e-6x O y = e-6x O None. O…

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Q: 2. Determine C when x-y%3D0 show the solutions. (xy + x)dx = (x²y2 + x² + y2 + 1)dy

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Q: Obtain the general solution unless otherwise instructed 3. (D² – 3D + 2)y = e2*(1+ e2x)¯1 SUMMARY OF…

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Q: (b) Consider the IVP, test whether it is exact and solve it. x(x – y)dy = -(3xy – y²)dx y(-1) = 1

A: Given differential equation x(x-y)dy= -(3xy-y2)dx   To test exact or not ,if it is exact then solve…

Q: (b) Solve the equation 2 = dy %3D -x+/x²+yz y(-3) = 4 for -3 <x57 taking the dx y step-length h =…

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Q: Find the general solution of the FOLDE, (x+ 3y)dx – xdy - 0. a. y= -2x + C b. Cx = 2x +y y--*+ Cx d.…

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Q: T:4x-34+2-2-0 Tz: dx+ Sy-32+4 = 0

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Q: Find ∫C (ez - 1) / z  dz with C being z(t) = eit for 0 ≤ t ≤ 2π

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Q: Question included in image

A: Given that,

Q: Q(2) Find the general solution of (2r2 + y)dr + (x2y-r)dy 0.

A: Solve the differential equations using exact differential equation method

Q: Seve: dy %3D e A Be

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Q: V9-r² S xydzdydx •3 (d) S So

A: We have to find value of given triple integration

Q: Q(5) Find the general solution of (r+2y- 4)dr - (2r +y- 5)dy = 0.

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Q: Find the particular solution for (2y3 – x³) dx + 3xy² dy = 0 when x = 1, y = 1 A. 5x?y³ = x5 + 4 B.…

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Q: Find the particular solution of an EDE (2xy2 +1)dx + (2x2y-y)dy%3D0 when x-2 and y=-2 Answer:

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Q: Q1) solve all these first order diff questions with appropriate method of solutions dy _ y²+xy?…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: C. Find for the general solution of the following DE. 8. (D3 + 3D2 – 4D)y = 0 9. (DA + 6D3 + 9D²)y =…

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Q: Given d'y dx² = 6x-0.5x², y(0) = 0, y(12)=0, Use step size h = 4, z1 = 20, and z2 = 25. Enter 4…

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Q: Y2 = Y1(x) / "dx (5) as instructed, to find a second solution y,(x). у" - 8y' + 1бу %3D 0%; Y1 = e…

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Q: ey-x y' = 1+ e2y ,y(0) = 3 %3D (h=0.01) .What is the error in the solution?

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Q: Solve the DE: 2(x+y) dx- x(x+2y-2) dy=0 A 2xy+ x2 = Ce* B 2xy-x²= Cey 2 ху - х2 - Се* none of the…

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Q: Use the method of reduction of order to find a second solution to t'y" + 2ty' – 2y = 0, t>0 Given y1…

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Q: Q6: Solve the following Higher-Order D.E. d³y d²y dy + 7- 5y = 0 dx 3 %3D - dx3 dx2 To find the…

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.