Homogeneous Differential Equation: (x* +2xy – 4y² Jdx – (x² – 8xy – 4y² kdy = 0 Use the substitution y = wx; d = wdx+ xdw

Q: y'=(9x+4y+1)2

A: Solution : I have used basic rule of differential equation.  For detail analysis please see both the…

Q: Q4: Use undetermined coefficient annihilator approach to solve. y"" – 5y" + 6y' = 10x² – 5x – 6 +…

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

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Q: Find the zeros. f(x) = x' - 4x2 + 3x + 2 %3D

A: Here given as fx=x3-4x2+3x+2put x=2f2=23-4×22+3×2+2=8-16+6+2=16-16=0⇒x=2 is zero of f.⇒x-2 is a…

Q: Integration

A: We will solve the integral.

Q: 5x-y2 2xy+3y2" c. xy? - 2x5 + 3y³ = C d. xy? + x5 + y3 = C 29. Find the general solution in implicit…

A: We have to find solution of exact differential equation.

Q: Determine a suitable form for Y(t) if the method of undetermined coefficients is to be used. y (4) +…

A: Introduction: The method of undetermined coefficient is a method to determine the particular…

Q: Higher Order D.E. -  Homogeneous Equation with Constant Coefficient

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Q: Find the general solution of the ODE. - y" - y' - 12y = 2xe-³x — ex

A: Given that the differential equation is                                          To find the general…

Q: Solve homogeneous equations (x³ +y³) dx -3xy² dy =

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Q: Solve for Z. X= (Y-Z) 3

A: Given: X=23Y-Z We have to solve for Z.

Q: Determine a suitable form for Y(t) if the method of undetermined coefficients is to be used. y (4) +…

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Q: Homogenous equation of higher order: Find the general solution to the following equation: y ''' +…

A: The given homogeneous differential equations, i) y'''+3y''-4y=0 ii) 2y'''-11y''+12y'+9y=0. We have…

Q: -4 -3 2 -1 -1 4 -2. -3+ y = x2 - 4 A y = x2 - 4x y = x'- 4 y = 23 4x - ©2021 Illuminate Education…

A: our answer is y=x3-4x

Q: Classify the equations below as separable, linear, exact, or none of these. Notice that some of the…

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Q: In Calculus you will see the symbol y'. Treat y' as a variable and solve the equation for y. 6y²y +…

A: To solve the following equation for y'. 6y2y'+30xy+6x2y'=5y2+25xyy'

Q: Solve the equation. (3x)dx+(2-3x³y ¹)dy=0 CIT An implicit solution in the form F(x,y)=C is-C, where…

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Q: Solve the equation (2xy+ y) dæ + (x² – x) dy = 0. - O y = cx(x +1)° + 2x O y = cx(x+1)¯³ – 2 II O y…

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Q: t dy dt a. Find y(40) b. Findt where y(t) = 900. 78. If = .08y (1 - y 1000) y(0) = 100

A: We need to find y(40) and t.

Q: Find the centroid of the plane area shown below using integration. y²= 3x - y = x²/3 -X

A: The centroid or geometric centre of a plane figure is the arithmetic mean position of all the points…

Q: 5. Exact Diffe re ntial Equation: x(3xy – 4y' +6}dx+(x' – 6x² y² -1dy =0

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Q: Write the following equation in the form w = u(x,y) + iv(x,y) h(z) = (3z + 2i) / (2z2 + 4)

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Q: Solve the IVP by substitution. (3x2 - 2y2)y' = 2xy;  y(0) = -1

A: Substitute  x = vy and than solve using method of separation of variables.

Q: solve for the homogeneous coefficient   (x²+2yx-4y²)dx-(x²-8xy-4y²)dy=0

A: Consider (x2+2xy-4y2)dx-(x2-8xy-4y2)dy=0⇒ (x2+2xy-4y2)dx=(x2-8xy-4y2)dy⇒dydx=x2+2xy-4y2x2-8xy-4y2To…

Q: Geberal solution of (3xy +3y - 4)dx+(x+1)²dy

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Q: Non Homogeneous LDE solve: (D2  +  D  -  2)y  =  2x  -  40 cos 2x

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Q: n m Find an integrating factor of the form x"y" and solve the equation. (3y³-8x¹y)dx +(4xy²-12y)dy=0

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