dy = ay – b dt

Q: Find dy/dx for y = J_1P+4 t2 dt t2+4 X. 3

A:

Q: dx x2+y?, dt dy 2, find dt dL when x = dt If L = V -5, and 7 and y = 6. dL dt

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Q: dx = x(1 – y) dt dy у(х — 1) dt

A: Solution of the problem as follows

Q: Find dy/dx: а. y = cos t dt

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Q: *show work*

A: Find dy/dx.

Q: Rewrite dx d?y + 3 +y: Sin t ニ dt? dt? dx -4X +S = Cost dz? dt

A: the approach follow:

Q: dy dt2 dt d'y 8x = 0 - dt?

A: Given that, d2xdt2+dydt=0d2ydt2-8x=0 Now take the derivative for the first equation with respect to…

Q: d'y dt? dy - +6y = 21° –t +3 ; y(0)=1, dy -(0) = 2 dt -5 %3| dt

A: At first, we have to find the complete primitive (C.F.) and then we find the particular integral…

Q: L[f(t)] = F(s) = [ e*“ f(t) dt -st

A: The given integral is a Laplace transform, it can be evaluated by the integral by parts method. Let…

Q: dx dy 1. +у%3х, Зу dt dt

A:

Q: dy dx Given y=x³ - 2× and = 3. Determine the value of dt when X=2. dt

A: Differentiate the equation y=x3-2x with respect to t. y=x3-2xdydt=3x2dxdt-2dxdt=3x2-2dxdt

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

A:

Q: Evaluate dx f(t) dt and * f(t) dt, where a and b are constants.

A: To evaluate: ddx∫axft dt and ddx∫abft dt, where a and b are constants. Solution: The fundamental…

Q: y = 2t + Vt dt J4 y' =

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Q: Find S t? e' dt using integration by parts.

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Q: (dx = x - y+z dt |dy = x +y – z dt dz — 2х — у dt

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Q: dx dy 5et %3D dt dt

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Q: d'y dy 4+y =r²-21 +3 dt? dt

A: We will calculate CF and PI separately then we will add them.

Q: Find dy/dx. x = t?, y = 1-6t dy

A: The objective is to find dy/dx.

Q: Find dy/dx

A: Given:y=∫0ex2 1t dtIntegrating formula∫xn dx=xn+1n+1

Q: Find dy/dx: a. y = cos t dt 0,

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: (e) dy if y = (t +1)(t + 9) %3D dt It%3D3

A: Given that y=(t2+1)(t+9)

Q: y = f VI + t? dt Y : 0. t2 dt

A:

Q: Find dy/dx: 1. y = J" cos t dt

A: Given

Q: 크(F(a+) e dt dx 19

A: We have to evaluate, ddxFx4=ddx∫10x4  e-t2 dt

Q: t²e*dt dz J2r

A: on solving this we get the

Q: dy =r-ky, y(0) = y, dt

A:

Q: dx dy %3D 2x + 2) + 1 dr dt dx +2 dt J+ 3 dt

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Q: Compute xe" dx + x?y dy along the curve x 3t, y = t2, 0 < t < 1.

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Q: Find dy/dx

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Q: dy - f *P, = 7 dt y(0) = 4.

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Q: dy Find dt y = (t sin t) dy dt

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Q: Find j cos(VF +1 +1)dt dx

A: Using the leibnitz integration problem.. Explanation of the solution is given below..

Q: dx = 5x + y; dt x(0) = 2 dy -3x + y; y(0) = 0 dt

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Q: find dy/dt. y = (t tan t)10

A: We will use the power rule, chain rule and product rule.

Q: Find: d/dt (xe^x)

A:

Q: dx/dt = X +y dy/dt = 2x + 2y

A: To solve dxdt=x+ydydt=2x+2y

Q: dy y? y(to) = 0 2t dt

A: Given                  dydt=-y22t,     yt0=0

Q: d (F(x^) = ew dt %3D dx dx

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Q: d t sec(t) dt dx

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Q: y=√x Find dy/dt, given x = 4 and dx/dt = 3 Find dx/dt, given x = 49 and dy/dt = 8

A: We have to find dydt given x = 4 and dxdt= 3 Find dxdt, given x = 49 and dydt = 8

Q: Find fa and fy. f(x, y) = 4e dt %3D

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Q: dx (b) (t– 2) – x = (t – 2)' , x(4)=10 dt dx (c) +5x -t = e" , x(0)= dt

A: Here we have to solve given initial value problem b and c.

Q: O1f y= x 4x and x = Vzr?+I, find dy /dt when t r2. %3D

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Q: Differentiate f(x) | Vt + sin t dt.

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Q: t (a) y = dt Vt? +1

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: find dy/dt. y = sec2 πt

A:

Q: y sin (r²) dt

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Q: dy -2y 3cos3t – 11sin3t dt? dt

A:

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.