dy = ay – b dt

Q: Determine whether it is stable or unstable. D) dx₁ dt = 3x₁x2-x1 + x2 dx₂ dt =x²-x₁

A: D Given system of differential equation is dx1dt=3x1x2−x1+x2dx2dt=x22−x1 We have to determine…

Q: Given the equation p=2x/y, find dy/dt

A: Using the properties of the logarithmic functions, it can be written that lnab=ln a-ln b. It is…

Q: 1?ei dt

A:

Q: ay ax px + y X

A:

Q: dy Find if y= dt 1 2 u+u and u = 9+ 5t.

A:

Q: d | Vsint dt dx 3 2.

A:

Q: dx The equation = cx, is separable. cx², dt Select one: True O False

A:

Q: dy If y (t+ 2t + 6) (7t + 6), r find dt dy dt

A: Given  y=t2+2t+67t2+6y=7t4+6t2+14t3+12t+42t2+36y=7t4+14t3+48t2+12t+36

Q: dy Find dt y = (4+ csc 2t) dy %3D dt

A:

Q: X = t + l 1 dt

A:

Q: dy Find for y = 9+ 10t2 dt. dw

A:

Q: dy If y = 2sin 3t then aY is: dt

A: we know that, derivative of a^x = lna * a^x  so from this we will solve the quesiton

Q: dy If y = sec? Va then dx

A:

Q: d Evaluate In(et – t²)dt. Briefly explain your answer. dx '1

A:

Q: dy Find dx, y= [v1+ ť dt

A:

Q: Find dt = 1₁ 5 y = 2 14 - 2t

A:

Q: Given y=pq, find dp/dt when p=30, q=250, dq/dt=-200, and dy/dt=-5250.

A:

Q: Sx³Vx2 + 12 dt

A: We have to evaluate the integral: ∫x3x2+12dx In this case we will use substitution method  let…

Q: [-+] 5t dy 3.1는-51%3D-y dt

A: This is a linear 1st order differential equation.

Q: dr Find dt

A: Given that r=s+1   and   s=16t2-20t. Obtain the derivative as follows.

Q: Find dy. y= /x+2 dy = (Simplify your answer.) %3D

A:

Q: d²x dt.² +2 d'y (1² - y = = cos 21. 2 da 9=0

A:

Q: + iwe¬lwt = 0. dt = 0,

A: Given differential equation is

Q: dv * + 4v = 0 dt

A: We have given differential equation,     We will find solution using separable method.

Family of Curves

A family of curves is a group of curves that are each described by a parametrization in which one or more variables are parameters. In general, the parameters have more complexity on the assembly of the curve than an ordinary linear transformation. These families appear commonly in the solution of differential equations. When a constant of integration is added, it is normally modified algebraically until it no longer replicates a plain linear transformation. The order of a differential equation depends on how many uncertain variables appear in the corresponding curve. The order of the differential equation acquired is two if two unknown variables exist in an equation belonging to this family.

XZ Plane

In order to understand XZ plane, it's helpful to understand two-dimensional and three-dimensional spaces. To plot a point on a plane, two numbers are needed, and these two numbers in the plane can be represented as an ordered pair (a,b) where a and b are real numbers and a is the horizontal coordinate and b is the vertical coordinate. This type of plane is called two-dimensional and it contains two perpendicular axes, the horizontal axis, and the vertical axis.  

Euclidean Geometry

Geometry is the branch of mathematics that deals with flat surfaces like lines, angles, points, two-dimensional figures, etc. In Euclidean geometry, one studies the geometrical shapes that rely on different theorems and axioms. This (pure mathematics) geometry was introduced by the Greek mathematician Euclid, and that is why it is called Euclidean geometry. Euclid explained this in his book named 'elements'. Euclid's method in Euclidean geometry involves handling a small group of innately captivate axioms and incorporating many of these other propositions. The elements written by Euclid are the fundamentals for the study of geometry from a modern mathematical perspective. Elements comprise Euclidean theories, postulates, axioms, construction, and mathematical proofs of propositions.

Lines and Angles

In a two-dimensional plane, a line is simply a figure that joins two points. Usually, lines are used for presenting objects that are straight in shape and have minimal depth or width.