Use Laplace transforms to solve the following initial value problem. - x' +2y' + x = 0, x' − y' + y = 0, x(0) = 0, y(0) = 121 Click the icon to view the table of Laplace transforms. The particular solution is x(t) = and y(t) =

Q: y''' -3y'' + 3y' -y = (e^x)(x+1) find the general solutions of this diff eq

A: Given differential equation is y'''−3y''+3y'−y=exx+1 Write the auxiliary equation  m3−3m2+3m−1=0…

Q: y" - 3y' + 2y = 2x² + ex + 2xe* + 4e³x

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Q: 12e* y' - 2y'+ y = 3

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Q: y"" - y' = 2e-* - 3e2x when x = 0, y = 1, y'= -1 and y" = 2

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Q: Find y'' in y = x(2x + 1)4

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Q: with y(0) -1

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Q: y''-7y +10=0, y(0)= 2 and y'(0) = 4

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Q: Determine y' of y = V4x+3

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Q: 4y'''+12y''+13y'+10y=0

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Q: x' = 2 -5 1-2, X

A: We will find eigen values and eigen vectors of coefficients matrix from given system and then find…

Q: y' + (=) y = xy²

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Q: 9-y" - 2y +2y=e; y(0) = 0, y(0) = 1

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Q: Find the derivative of y= (2x³+x+1) 4(x²+3)5 (x4+3) 3 O A dy (4) (2x³+x+1) ³ (5) (x²+3) 4 dx 2(x²+3)…

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Q: find y as a function of x if: y'''-13y''+42y'=60e^x, y(0)=11, y'(0)=24, y''(0)=21

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Q: x²y' = 4x² + 7xy + 2y²

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Q: 3. y'+7=(-2x+ y)';y(0) = 0

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Q: y = 5** +(3–x²)

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Q: xy' = 3y + 8x, y(2) = 8. y= ((8x^8/8)+3)x^3

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Q: 2x5y ' = y(3x4+y2)

A: For the solution follow the next step.

Q: y'-(2/x)y=(y^3)/(x^2) find the solution that satisfies y(1)=1

A: The given differential equation is

Q: Find y" * y" at (1,1) of x'y =1

A: We have to find derivative

Q: y''''' - 3y'''' + 3y''' - y" = 0

A: To solve y""'-3y""+3y"'-y"=0

Q: Find the derivative of y = 5x²sec 1(2x-3). O y'= 10x sec-¹(2x-3) + O y'= 10x sec-¹(2x-3) + O y'=…

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Q: Find the derivative of the following: y = 2x* + + 3a? – 7 O y' = 8x³ + a² + 6x O y' = 8x + 2æ² + 6x…

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Q: Find y'when ye2x = 3y+ x and y(0)=3 (A) -5 B B -6 (© -4 D) -7

A: We need to find y'.

Q: Get the first order derivative of the function x + sin(y – 2x) - 1= 0 - 2 1 a. y' = cos(y-2x) 1 b.…

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Q: Find y''' for y = 1/(x+4)3

A: To find the first derivative, y' of y, differentiate (x+4)-3 with respect to x, using the general…

Q: _____18) Find y' if y= 6+x √4-x²

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Q: x 3y'''- x 2y'' + 2xy' - 2y = x3

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Q: 2. (x2) y = y+2(x2)

A: Topic = Differential equation

Q: y""+12y" +36y=0; y (0) = 0; y'(0) = 1;y" (0) = -7 ✓y""+y" - 2y=0 y" - 4y'-5y=0; y ( 1) = 0; y' (1)=2…

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Q: If Ax) = 2x+ 1and g(x) = x, Find g0)) %3D

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Q: can you explain if this is true or false if y=x2+y2, then y'= 2x+2y

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Q: y''''' + 8y''' + 16y' = 0

A: Given differential equation yV+8y'''+16y'=0 We have to find the general solution of the given…

Q: Substitute the value of y' in 1 + (y)²

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Q: |_y'''+12y" +36y'=0; y (0) = 0; y'(0) = 1;y" (0) = − 7

A: Since you have posted multiple questions, we will provide the solution only to the first question as…

Q: y(t)=(2t-1)(5t-5)^-1, find y'(t)

A: Using Quotient Rule of Derivatives

Q: y”+y’=0; y(0)=-4 , y’(0)=6

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Q: Find y'. y = [In(x5 + 3)]2 y' =

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Q: Find y as a function of a if = y"-7y" +12y = 6e², y(0) = 24, y' (0) = 16, y" (0) = 27. y(x)=

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