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

Q: Find the solution. (D2+4D+4)y=0; when x =0, y=1, y'=-1. Ay = (1 – x)e2r y = (2 + 3x)e- y = (1 +…

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Q: 2. obtain the general solution. a.(D² – 3D + 2)y 2x- 9x + 6x. b.(D + 4)y = 5e - 4x. c. (D² + 4)y = 5…

A: (b).   The given differential equation is: (D2+4)y=5ex-4x

Q: Find the general solution by variation of parameters y" – 10y' + 25y = x3 |

A: Given: y''-10y'+25y=e5xx3

Q: (D² + D)y =x+| ;

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Q: Solve the given equation.. dy - 3y = x³, v(1) = 10 X dx a. y(x)= x²Inx+5x³ b. v(x)= x?Inx + 10x³ c.…

A: Please refer to the image below

Q: Use variation of parameters to find the particular solution to y'' - 7y' +12y = 3e³t Y(t)= Preview

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Q: Find the solution of the D.E. below: 2(2x² + y*)«x – xycdy = 0 ... x* = c (4x²+y²) x* = c(x?+ 4y?) B…

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Q: 2. Use the mothed of variation of parameters to find the general solution of the following…

A: We can solve this using variation of parameters for three variables

Q: (9x-4y+4)dx-(2x-y+1)dy=0

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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: Q2/ A/ Find the equation of straight line passing through the point (1, 2) and parallel to the line…

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Q: Obtain the general solution of the following equations:    2y(x2-y+x)dx-(x2-2y)dy=0

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Q: The solution of (D² – 4D+13)y 0 5 2x (A eix . Be Jox (A ex + Be)

A: D2-4D+13y=0 The auxiliary equation is m2-4m+13=0 ⇒m=4±-42-4132⇒m=2±3i

Q: solve this linear equation using gauss seidel x+ y−z=0 2 x−3 y+z=1 2 x+ y+2 z=7

A: The given equations are; x+ y−z=02 x−3 y+z=12 x+ y+2 z=7

Q: x+y-4) dx-(3x-y-4)dy=0; when x=4, y=1 Solve using Coefficient linear in the two variables

A: ( x+y -4)dx-(3x-y-4) dy = 0 , x=4                                                               y…

Q: Use the method of variation of parameters to determine a particular solution to the given equation.…

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Q: Obtain the general solution. (xy + x) dx = 2 2 y + x + y¯ +

A: The given differential equation is…

Q: SOlve the differentilal equation d²y d*y 4- d³y + 7. dx2 14 | dx+ dx3

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Q: Solve and find the domain in which the solution is defined. dy/dx = (y2-xy-x2)/x2 , y(-3)=-6

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Q: Obtain the general solution. (D^2- 2D + 2)y = 0

A: Using solution of Linear Differential Equations with constant coefficients.

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: dw 4w A) Give the general solution of dx = x³. B) Solve y' + = y²x³.

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Q: In the given question , find d2 y /dx2 implicitly in terms of x and y:-   x2 y - 4x = 5

A: Given: x2 y - 4x = 5 Now differentiate with respect to x we get,…

Q: e2x-ydx + ey-2×dy = 0

A: e2x-ydx+ey-2xdy=0⇒e2x-y+ey-2xdydx=0Substitute  dydx with y' ⇒e2x-y+ey-2xy' =0⇒e2yy'…

Q: Find the solution. d3x d?x d³x dx + 2 =0 dr3 dr? dt

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Q: 1. (y-x+ xycotx)dx + xdy = 0 2. xdy + (1 – 3x)ydx = 3xdx

A: .

Q: Q1: using variation of parameters to solve: * y"' – 2y" – 21y' – 18y = 3 + 4e-t %3D

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Q: In the given question , find d2 y /dx2 implicitly in terms of x and y :- x2 y - 2 = 5x + y

A: Differentiation of the function with respect to x helps to find the derivative of the function.…

Q: What is the general solution of ху(ху? - 1)dx + х?(1+ ху) dy3D0 ? A 2x3y5-3x2=c B 4x³y7 +3x? = cyA ©…

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Q: y" + 2lf + 2y = 0, y(0) = 1, f(0) = 1 he solution as a linear combination of y, and y2-

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Q: y" – 6y' + 9y = :

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Q: What is the general solution of ху(ху5 - 1)dx + х?(1+ ху)dу%3D0 ? A 2x°y³ - 3x² = Cx? B 2x?y5- 3x? =…

A: Solution: The given equation is  xy(xy5-1)dx +x2(1+xy5)dy=0

Q: Which of the following equations is variable separable? O a. (3a2 – y²)dx – 2aydy = 0 O b. (z² +…

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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: Obtain the general solution unless otherwise instructed . (D² − 3D + 2)y = e²x(1 + e²x) −¹ Yc = Ур =…

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Q: Find the solution of 2xV dx +y =x is O a. Wx = + C 3x½ +C O b. 2x2 +C 5/2 d. Wx = X + C 3.

A: Given, the differential equation,2xdydx + y = xDividing by x on both sides, we getdydx + y2x = 12It…

Q: What is the solution of (2x - y)dx + (4x + y– 6) dy = 0? а. (x+у-3)°- с (2х +у- 4)? b. (x-y+3)²=…

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Q: Obtain the general solution unless otherwise instructed a.) (9D4 + 6D3 + D2)y = 0 b.) (4D4 − 45D2…

A: (a) Consider the given equation. 9D4+6D3+D2y=0 Convert the equation into the characteristic equation…

Q: Find the solution. dy x-+5y=2x3y4 dx A y = -x+Cx13 15 6. -2-cx 15 23 B y = CX x²+cx 15 y = -

A: Given differential equation is xdydx + 5y = 2x2y4

Q: d²y 4y 3e2x. %3D dx2 3.

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Q: Solve (2a² + y) dæ + (x²y – x)dy = 0 %3D 4:x + y² – 2yx-1 = C 2y+ 4x² – xy¯= C xy' = C - Option 1 O…

A: Given: 2x2+ydx+x2y-xdy=0

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: Find the general Solution of DES 2x y Y' = x? +2y} %3D

A: SOLUTION-

Q: 2. obtain the general solution. a.(D - 3D + 2)y = 2x – 9x2 + 6x. b.(D2 + 4)y = 5e - 4x. c. (D² + 4)y…

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

Q: Show solution how to find d2y/dx2 , d3y/dx3 , and d4y/dx4  when The given is x = t3 + t and y =…

A: Given: Show solution how to find d2y/dx2 , d3y/dx3 , and d4y/dx4  when The given is x = t3 + t and y…

Q: Obtain the general solution. x² + y?. (xy + x) dx = (x¯ y´ 2 2 2 + x + +

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Q: Determine the value of C if f(x,y) = C is the solution of (x+ 2y-3)dx+(x+2y+1)dy3D0 for x=94 and y=…

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