In differential equation, how to answer family of curves in process and determining the solution of the family of curves easily?

Q: y' = (y² - 1)(e-2) where, y(0) = 3 2 and y(0) = -4

A: Given: The  differential equation is y'=y2-1ey-2 and   y0=32 , y0=-4. Plot the graph of the solution…

Q: (3y²-x 0 ;when x = 1, y = 1 2y4

A: This is homogeneous Differential equation

Q: How differential equations and may lab helps in architectural engineering field

A: MATLAB is a computer program that provides the user with a convenient environment for performing…

Q: Find the general solution using separationof variables y = re" y = 5ry – 2r Solve r dy = y +1 and…

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Q: Straight lines with sum of intercepts equal to 10. Find the differential equations

A: Given:Straight lines with sum of intercepts equal to 10

Q: (D³ – 3D² + 2D)y e 3x | 1+ex

A: Solution:-

Q: (2 − x²) y" + 2xy' – 2y = 0 (a) Verify that y = x is a solution to the above equation. (b) Find the…

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Q: Why are separable differential equations called "separable"? State an application of these types of…

A: Suppose we have a differential equation involving x and y as variables. Separable differential…

Q: The solution to the differential equation (x²2 -4xy-2y²)dx+(y² -4xy-2x²)dy=0 a. y²(y-6x)+x²(x-6y)=c…

A: To find the solution of the following differential equation. x2-4xy-2y2 dx+y2-4xy-2x2 dy=0

Q: Example of a differential problem illustrating two (2) or more possible solutions.

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Q: Dx + D°y = e* » (D+1]x+(D-1)y= 4e* %3D

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Q: xy' + (1 + x)y = e* sin 2x %3D

A: xdydx+1+xy=e-xsin2x

Q: Straight line whose y and x intercepts are equal

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.