Ex.: Solve (2D+3D-9)x+(D² +7D-14) = 4 (D+1)x+(D+2)y= 0 (2)

Q: Solve (D³ + 3D² + 16D - 20)y=0 when x = 0, y = 1, y = 0, y" = 1

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Q: Solve the IVP. y'-7y(6-y), (0) = 5 %3D y3=

A: Given  y' = 7y(6-y)dydx = 7y(6-y)dyy(6-y) = 7dx                              (1) We will solve it by…

Q: Find the Solution of the ff: 1. (D³ – 3D² – 3D + 1)y = 0

A: As per our guidelines we are supposed to solve only one question i.e. the question no (1). For the…

Q: Find the general solution (D4+2D3-6D2-16D-8)y = 0

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Q: Solve for y: (D^3 - 3D^2 + 3D - 1)y=0

A: The solution are next step is

Q: Solve (D3+2D2-3D)y=x.e3x

A: Given: The given differential expression is a non-homogenous linear differential expression. The…

Q: Give the general solution of (D5 - 3Dª + 8D² – D – 5)y = 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: solve for (D³ -9D)y=0

A: If roots m1,m2,...,mn of the auxiliary equation is real and distinct then complete solution is…

Q: Solve [D* +3D² –-4]y= 2sin° (5x)

A: Solution of non Homogeneous differential equation

Q: Obtain the solution 3. (D³ - 2D + D- 2)y = 0

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Q: 25x2+16y2-600x-256y+4224=0 What is the standard form of the equation?

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Q: (D³ -3D* +4D³ -8D² +16),y = 0

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Q: Determine the solution of ( D3 - 4D2 + 3D)y = 0

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Q: Find the general solution (D3+3D2-4)y = 0

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Q: Solve the equation (D² - 3D + 2) y = 2x² + 1 Oy=c₁e² Oy=c₁e* + c₂e² + 3 + 4x + 5x² + c₂e²x + 4 + 3x…

A: Solving the differential equation below

Q: x² 2. y- 3D1 4)

A: 2) standard form of hyperbola (y-k)2a2-(x-h)2b2=1   ....(1)given y2-x24=1(y-0)212-(x-0)222=1…

Q: The particular solution of (D³-5D + 4)y = 0, when x = 0, y = -2, y' = 8, y" = 0

A: Since you have asked multiple questions so as per guidelines we will solve the first question for…

Q: Give the general solution of (D5 – 3D4 + 8D² – D - 5)y = 0,

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Q: Solve graphically:                                    2x – 3y + 13 = 0 and 3x – 2y + 12 = 0

A: Given,

Q: 12.xe y = V3x + 2

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Q: find the solution (D^3-3D-2)y=0 when x=0, y=0 and y'=9, y''=0

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Q: Solve. x+ y+ z = -7 2x + 5y + 2z - 32 %3D -x+ 7y- 3z = - 41

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Q: (D² + 3D + 2)y = 12x²

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Q: Find the solution, (D3-3D2+30-1)y = 0

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Q: X+4y-z х+у-6z %3D -12 3x-y-z = 4 -5

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Q: Give the general solution of (D5 – 3Dª + 8D² – D – 5)y = 0

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Q: Find the general solution to(D5 - 2D3 – 2D2 – 3D - 2)y=0

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Q: Find the solution of (D²-4D+5)y=0.

A: We first find roots of auxiliary equation then we write the general solution.

Q: ai) Solve explicatly dy zy 2X txe 17 =

A: Given equation is dydx=2yx+x2ex, with initial condition y1=0. Solve explicitly.

Q: What is the solution to the equatio 2y+6 :-10 %3D -2

A: Cross multiply and solve

Q: (D³ - 3D² - 6D + 8)y = xe

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Q: -2 -1 1 y -7 -2 13 m = b%3D Equation: 3.

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Q: Find the solution. (D4 + 3D3- 6D2. 280 -24)y = 0

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Q: The solution of y – 6y – 2y = 0 is -

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Q: b) y' - y = 2x3 y(1) = 1 | c) y' -8x3y e2x* y(0) = 2

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Q: Find the solution. (D³+3D²– 4D)y = 0

A: The Auxiliary equation is D3-3D2-4D=0 solve for D D3-3D2-4D=0 DD2-3D-4=0D=0 or D2-3D-4=0 now…

Q: (D³ – D)y 3x %3D -3x2 а. Ур -3 2. b. Ур 3x2 +3 2. С. Ур -3x2 +2 3x2 d. yp 2. ||

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Q: J -dp- 2x² +3x + 1

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Q: Find the general solution (D3-3D2-3D+1)y = 0

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Q: Find the solution. (D5- 2D3- 202- 3D - 2ly = 0. A y - (e,+ele. O y - (e,+e

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Q: 2y %3D The solution of y - = 3x2 is

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Q: = 0

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Q: Solve the equation. Wx+3 3D x - 3 X -3

A: Here the given equation is Squaring both sides of the equation

Q: (D² – 3D + 2)y = 2x3 – 9x2 + 6x. Find the solution. * c,e* + c2e2x + x³ + 1 ce* + cze2* +x³ ce* +…

A: Second option is correct

Q: Find the Solution of the ff: 3. (D³ + 2D² + D + 2)y = 0

A: Topic = Differential equation As per guidelines , At a time only one question can be answered.…

Q: x+y=D4 2. x-y%3D6

A: Given that, There are two equation following, x + y = 4…

Q: 14. 2x2 – x³y' = y3 %3D -

A:

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.