Solve algebraically forx, and y a. x2+ y2 25 x+y= 1 b. y2-x2 16 3x + 5y 16 %3D

Q: 1. (2х — 5у + 12)dx + (7x — 4у + 15)dy %3D 0 |

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Q: Solve y"+2xy' = X Y(0) =1, y'10) = 2. Use erf(x) in your solution.

A: Given equation is, Now, substituting then,

Q: Find a real general solution. x?y" – 2y = 0.

A: The given differential equation is x2y''-2y=0. Clearly, the given DE is a second order Euler…

Q: 5. Solve the IVP: 2 y' +=y = -x°ys; y(-1) = 2 A. 16 = y*(32x10 – 31x®) B. 16 = y*(32x10 + 31x®) C.…

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Q: a) Solve (t3 + y³)dt – ty²dy = 0

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Q: (D² + D)y =x+| ;

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Q: Find the general solution. 1. (D2 + 3D − 18)y = 0

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Q: y? + 3xy Solve the IVP y' y(1) = 5 using appropriate substitution. x2

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Q: y=Cie3x + C2e¯ 2x + x

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Q: Find the general solution of (D3 – 2D2 + D)y = x

A: (D3-2D2+D)y=xlet D3-2D2+D =0D(D2-2D+1)=0D(D-1)2=0 D=0 or D=1,1Therefore C.F.=C1+C2ex+xC3exnow we…

Q: AXPS ADNF. Solve for x and y. y D 54 4y-3 51 S. 57 17x+3

A: Given data: ∆XPS≅∆DNF The length of XP=4y-3. The length of XS=17x+3 The length of NF=51. The length…

Q: y3 (x+c)e* is a solution of y-y3e"* A True B False

A: To show y=(x+c)e-x                     (1) is a a solution of y'-y=e-x                      (2) Then…

Q: Which of the following is the general solution of the DE y" - 12x?? a y-x- Cx +C b. y-+Gx + C, C…

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Q: Find the general solution of y' = xy². а. у(x? + с) + 2 3D0 c. (x² + c) + 2 = 0 e. none of the…

A: Given differential equation is y'=xy2

Q: Determine whether y=x-1 is a solution of V)'+y=-1

A: Given y=x2-1, taking derivative with respect to x. ⇒dydx=ddx(x2-1)⇒y'=2x-0  ∵dydx=y'⇒y'=2x…

Q: Find the general solution for y' = y – xy³e-2x А. 2ye2x — — х? + с B. e2x = y2(x² +c) C. 9e2x = y²…

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Q: Find the general solution of the BDE, y' = a. y=1-Cx 2x2 b. y= 1+Cx С. у3 1+Cx2 2x d. y= 1+Cx2

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Q: 4. (х + у — 1)dх + (2х + 2у + 1)dy — 0

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Q: OBTAIN THE GENERAL SOLUTION (y? - - ) 1. 3 y + (2 y - 3) dy = 0

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Q: Find the general solution for y' = y – xy³e-2* A. 2ye2x = -x² + c B. e2x = y²(x² + c) C. 9e2x =…

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Q: bx-'x5/cxfx1 b-1 (x"x/c 1/b (e) 6x0.2 = 5y0.4 (solve for y in terms of x) %3D x = (2-1/2)-1/2 (solve…

A: Since you have posted multiple sub parts, as per our policy we will answer first three subparts.…

Q: (ху+ усotx)dy — у(хdу+ ydx) 30

A: Given the differential equation             (xy+ycotx)dy-y(xdy+ydx)=0

Q: The solution to the equation is ged (D²-D-6)y(x) = xe %3D 1 1 -xe" (5x-2) - y,(x) 50 1 د. غير ذلك…

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Q: 11. (D- D)y = 0.

A: As per our guidelines only one question can be solved. Please find the solution for Q no 11 below:

Q: Find the solution of y − y = e2x , y(0) = 1.

A: Substitute value of the variable given in the equation. Then after calculation the value of other…

Q: Find the particular solution of r*y – y y+1 ; y (3) = -1

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Q: [x + y) dy = (x - y) dx x²

A: We need to solve D.E.

Q: Find the particular solution. y' = e = 8; y(0) = 7

A: Given Data: Differential equation: y'=ex-8 ......(1) Initial condition: y(0)=7 Integrate the…

Q: Find the solution. y' = y - xy³ e-2x A e2=x²(y²+c) B e2Y =x²(y²+c) (c) edx =y²(x²+c) (D D e=y²(x²+c)

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Q: Solve  x+y=a+b  ax-by=a2-

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Q: (x+ 1)y' – 2(x? + x)y = y(0) = 5

A: As per the company guidelines we can solve first question. I hope that the given solution will help…

Q: y(x) =xr,  with r satisfying r2 + (b - 1) * r + c = 0, it's the equation solution of x2 y''…

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Q: The particular solution of xyy' = (x² + y²) when x = 1, y = 2 is a. y2 = x² In x² + 4x² b. y2 = x In…

A: Given:- xyy'=(x2+y2)  To find:- Particular solution of given differential equation when x=1 and y=2

Q: Find the complementary solution: (D^3+D)y=x

A: QUESTION- Find the complementary solution:   (D^3+D)y=x

Q: Which of the following is the general solution of the DE y" = 12x? a. y-x*- Cx + C b. y-+ Cx + C c…

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Q: Solve the equation for y: ax + by = c

A: We have to eliminate the term 'y' and thus we get the solution.

Q: Find the general solution 5. (D² – 1)y = 0

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Q: y=c1J3(/3x) +C2J3(/3x)is solution for x?y"+xy'+ (9x-3) y=0 ylgn ihi

A: True

Q: Solve for x and y:                                     ax + by = a – b and bx – ay = a + b

A: given:

Q: Solve the general solution 3x² ydx + (y* - x*) dy = 0

A: Solved below

Q: Solve y"-xy' - By = 0, x>0 A) y = e+ B) y = c,x* + C) y= + D) y =c,3r*+

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Q: ii) Solve (x D²– 3xD+4) y = x² given that y(1) =1 and %3D - y'(1)= 0.

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Q: The solution to the equation is ged (D²-D-6)y(x) = xe %3D 1 1 1 e* (5x + 2) -7 y,(x) = - t xe" (5x +…

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Q: Solve the IVP: y" + y' = 0 y(n) = 0, y'(1) = 2, y'"(n) = -1

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Q: Find the general solution y" + 3y + 2y = 3e-t cost + 4e

A: To find the general solution of the given differential equation

Q: Find the solution. y' = y - xy3 e-2x A e=x?(y²+c) (A) (в B e2 =x²(y²+c) © e2» =y²(x²+c) e2x…

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Q: Find

A: The given equation is: (y-zx)p + ( x+yz)q = x^2 + y^2

Q: Q3/ A: Use the method of separation of variables to solve the equation x +1 y - y'e".u = 0

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Q: Find the general solution. (x³+3xy²)dx + (y³ +3x²y)dy=0 O a. x4-y4-6x²y² = c О а. O b. x*+y*+6x?y? =…

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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.