B. Homogeneous DE with Constant Coefficients - Auxiliary Equations (Repeated Roots) 4. (4D5 – 15D3 - 5D? + 15D + 9) y = 0

Q: B. ty" – (t+ 1)y' +y = t?

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Q: 3. Solve, using the method of variation of parameters: y" + 4y' = sec 2x

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Q: () = (5y – 2x) y' – 2y = 0; y %3D | 4 II

A: Exact differential equations

Q: y" + y' - 3y = 4sin 2x

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Q: [2] Determine homogeneous the roots of the auxiliary equation y=x²-ecosx for a linear equation with…

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Q: 2. y() + 2y" - 2 А. 1 В. 2х C. x? D. ½ x?

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Q: y"- y' = 4e-* +3e2x: y(0) = 0,y'(0) =-1, y"(0) = 2

A: We have to solve the equation using method of undetermined coefficient.

Q: – kz = 0, -z= 0, solution then

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Q: How to solve this equation y'''+2y''+4y'+8y=5e^(3t)+1 using Variation of Parameters

A: Consider the given equation. y'''+2y''+4y'+8y=5e3t+1 Find the characteristic equation.…

Q: Q1 Using a method of reduction to separable equation and reduction to linear equation, find the…

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Q: (Dª + D² + 10D)y= 0 , y(0) = 0, y'(0) = 6, y" (0) = 4, y"(0) = 4

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Q: Solve, using the method of variation of parameters: et y" – 2y' + y =: 1+x²

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Q: 2xdx + (y – 2x)dy = 0 (x+ y)dx + xdy = 0

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Q: Solve second order DE y" - 4y' + 4 = 0

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Q: y" - 5y' = x - 2, when x = 0, y = 0, y' = 2

A: We have to solve the given differential equation.

Q: Solve using characteristics of equations. 4. 4y" + 24y' + 37y = 0 ; y() = 1: y'(1) = 0

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Q: Determine the roots of the equations using iterative methods with initial values of 1. 2х + 6у + 32…

A: Gauss-Seidel method is used to approximate the solution of a system of linear equations by…

Q: solve using the appropriate method.xy = 2y + x − 1, y (3/2) = 9

A: We have a function in two variable (x,y)  and a value at particular x. we can separate y and x both…

Q: B. Non- homogeneous Higher Ordered LDE 2 1.D +50² + 8D -9) y - 69x²e-*

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Q: Solve the nonhomogeneous equation using the method of undetermined coefficients: y" – 2y' – 3y = 4x…

A: First we will find the complementary solution using the roots of the auxiliary equation then using…

Q: 3y = 3xy' + y'3

A: Solution: Here 3y=3xy'+y'3 Divide both sides by 3 y=xy'+13y'3   ......(1) Let dydx=P Then from…

Q: Solve using the method of variation of parameters: y" + 9y = 12 sec 3x. %3D

A: Solution :-

Q: Solve 5y'" – 28y' + 15y = 0, y(0) = - 4, y'(0) = – 24.4 %3D y(t) =

A: Given: 5y''-28y'+15y=0, y(0)= -4, y'(0)= -24.4

Q: Solve using characteristics of equations. 4. 4y" + 24y' + 37y = 0; y(n) = 1; y'(1) = 0

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Q: Use the method of separation of variables to solve : xyu̟ +2u, = 0, Q.4 U(x,0) = 3x*.

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Q: The following equation is a Homogeneous equation - (y/x form). Use the variable substitution u = y/x…

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Q: (2x+3)y'= y+y²(2x+3)^½ Linesr equation or bernoulli equation

A: The given differential equation is 2x+3dydx =y+y22x+312. The standard form of Bernoulli's…

Q: 3. Solve using the method of variation of parameters 1 y" + 3y' + 2y = 1+ ex

A: Solution is given below:

Q: Use an appropriate substitution to solve the equation z15 and find the solution that satisfies y(1)…

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Q: Solve using the method of variation of parameters 1 у" + Зу' + 2у 1+ e*

A: Using method of variation of parameters

Q: Solve the homogeneous equation (x²+y²)dy + x²dx = 0 Please help.

A: x2+y2dy+x2dx=0rewrite in standard format x2+y2dy=-x2dxdydx=-x2x2+y2

Q: Obtain the second solution of the given equation. (1–2x-x*) y"+2(1+x) y'-2 y=0; where y,=x+1

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Q: solution for z(x, 0) = x², z(1,)

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Q: y" + y = 0, y(0) = 0, y' (5) = 2

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Q: A. Homogeneous DE with Constant Coefficients - Auxiliary Equations (Distinct Roots) 5. (4D4 + 4D3 –…

A: Given: (4D4 +4D3 -13D2  -7D+6)y To find the auxiliary equation.

Q: b, Solve dy- y -n3y²--x5 finding particular solution.

A: Solve DE

Q: B. Homogeneous DE with Constant Coefficients - Auxiliary Equations (Repeated Roots) 2. (D4 + 6D3 +…

A: Given that: D4+6D3+9D2y=0  . Therefore, D4+6D3+9D2=0or, D2D2+6D+9=0 So, the above equation should…

Q: Solve using method of variation of parameters: y" + 2y' - 8y = 2e-2x - ex, y(0) = 1, y'(0) = 0.

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Q: Solve method of undetermined coefficients using (D+AD+8)Y 3X t, z 13e +50X when x-0, y=0, Y=D0 ゾーo

A: Given that, D2+4D+5y=13e3x+50xwhen x=0,y=0,y'=0

Q: Solve the nonhomogeneous equation: (D2-4)y = 2 –8x, when x=0, y=0, y’=5, using undetermined…

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Q: Solve the DE using the method of variation of parameters: *y" 4ry' + 6y-6a, y(1) –3, y'(1) =2 All…

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Q: dz = 4y-7z 52-9

A: First we will show that the given first order differential equation is homogeneous then by using the…

Q: 3. Solve using the method of variation of parameters 1 y" + 3y' + 2y 1+ e*

A: First I have find the auxiliary equation and using it find the complementary function and then by…

Q: 4. Solve y 3x 3y + 2y" e using undetermined coefficient. Show all the work.

A: We need to solve D.E.

Q: B. Homogeneous DE with Constant Coefficients - Auxiliary Equations (Repeated Roots) 3. (4D4 + 4D3 –…

A: To find the solution of homogeneous differential equation 4D4+4D3-3D2-2D+1y=0, find the factors of…

Q: Solve using the method of variation of parameters y" + 3y' + 2y =: 1+ e*

A: Given that: y''+3y'+2y=11+ex

Q: Solve by homogeneous equations method (x² - 4xy - 2y²) dx + (y² + 4xy - 2x²) dy = 0

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Q: y" + y' - 3y = 4sin 2x %3D

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Q: = -y² + 2x²y + 2x – xª, y1 = x² %3D

A: The Riccati equation is of the form