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

Q: Calculate y" and y'''. y = 4t 3 - 9t 2 + 7

A: Given that  y = 4t3 - 9t2 + 7 We have to calculate y'' and y'''. First we find y'. y' = ddty     =…

Q: Solve , y" - 8y' + 12y = 0

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Q: Differentiate. x4 y: 3 — х3 y' У -

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Q: Solve y”+9y = 2sec(3x) using the method of variation of parameters.

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Q: Solve ,  y" - 6y' + 8y = 0

A: Given differential equation; y" - 6y' + 8y = 0

Q: Solve in variation of parameters y´´ + y =cscx

A: Given differential equation is: Solution of differential equation is sum of complementary function…

Q: d) Find a minimal spanning tree in the following weighted graph using the Prim's algorithm. V7 V6 V4…

A: As per the Prim's algorithm first in the given graph G, we need to remove the loops and parallel…

Q: Solve xy"- y' - 4x³y = 8x³sin(x²).

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Q: Solve ,  y" - 8y' + 15y=0

A: Given a differential equation, y''-8y'+15y=0

Q: Use method of variation of parameters. y" +2y-8y = 2e-2x - e-x.

A:

Q: Solve ,  y"-7y'+12y=0

A: Given  y''-7y'+12y=0→             1

Q: Solve by variation of parameters: 2x²y" +5xy' + y = x² - x

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Q: What is the order of the equation y" y- (y')³=4?

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Q: Solve ,  y"-12y'+35y = 0

A: We have to solve  y" - 12y' + 35y = 0  (D2 - 12D + 35)y = 0 The auxiliary equation is  m2 - 12m + 35…

Q: y= Sinh (3x+5x+6) 2. %3D

A: We have to find differentiation of the given function.

Q: Solve:  y’’’ – 4y’’ + y’ + 6y = 0

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Q: * Salne the equalion:- (2x-44 +5)y'=n -2y+3

A: This homogeneous differential equation is solve by substitution and then by separation of variables…

Q: Solve y" - 2y" +9y' - 18y = 0.

A: Given differential equation: We have to find the solution of the given differential equation.

Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.