dx a. dt b. 2y dt

Q: S dy(t) = y(t) = - iw ſe-iwt dt.

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

A:

Q: Set dx dy where

A: We have to solve given problem:

Q: d t In(t)dt} dx 3

A: We will find out the derivative of given function using fundamental theorem of calculus.

Q: Find dy/dx

A: Using the second fundamental theorem of calculus and the chain rule we get

Q: e`y? dy = VT

A: We will reduce the domain of integration by observing the fact that, e-y² is an even function. Then,…

Q: The value of yx +y dx dy

A:

Q: S(xcos?x + xsin?x)dx jt la

A:

Q: dI +I= e* dt

A:

Q: d 17. t?e" dt dx

A: We have to solve

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

A: the approach follow:

Q: dx – x = 4y, UTM dt dy + x = y + 3e', dt

A:

Q: dt dy 글 + 1y dt

A:

Q: Find the value of dw/dt if w = x2+y2, x = 26 cost and y = 26 sint

A:

Q: 1. Jxe dx

A: We have to apply simple integration rules to solve the problem

Q: Js xng" dy dy

A: In general, the integral of a real valued function f(x) with respect to a real variable x on an…

Q: a - Find h (Stet sinh t sint dt)

A: The objective is to find ∫te-3tsintsinhtdt It is known that, sint=et-e-t2isinht=eit-e-it2…

Q: · ||r(t)|| 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: e*dx 19) J+ ex + e2x

A: See the details solution in below

Q: If y = x + ex, find dx/dt.

A: Given query is to find the derivative of the expression.

Q: 2. [ xsec’x cot xdx tamol svode se gniau s 3. ftsin2t dt

A: Disclaimer: “Since you have asked multiple questions, we will solve the first question for you. If…

Q: dx dy 5et %3D dt dt

A:

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: dy Find dx, y= [v1+ ť dt

A:

Q: dy = ay – b dt

A: In this question, we solve the differential equation by reducing into two-part.

Q: dx dy 1. " + y = x , dt = 3y dt |

A:

Q: L{S t? cos t dt}

A: Note: Hi! Thank you for the question as per the honor code, we’ll answer the 7th question.  Please…

Q: Calculate dy/dx at the point indicated. c(t) = (t^3 + t, t^2 − 1), t = 3

A: Given: Ct=t3+t, t2-1 at t=3

Q: c) L{S,T sin t dt

A: Given,          ℒ∫0tςsinςdς

Q: t²e*dt dz J2r

A: on solving this we get the

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

A:

Q: 2 dy + y? = ty %3D dt

A: We have to find the general solution of the given differential equation. We can rewrite the…

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

A:

Q: LL y e* dz dx dy -Inx

A:

Q: Find dy/dx

A:

Q: d Calculate dx dt

A: We have to calculate given identity: Concept:

Q: dP Р(а — ЬР), Р(0) — Ро wherе а,b and Po are constants dt

A: Where Po ,a,b are constants

Q: dy if x = In(csc y +c dx Calculate

A:

Q: Salve: (1+yjdx =2yVi-x? dy

A:

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

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

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

A:

Q: d t sec(t) dt dx

A:

Q: dy + y = ť°, dt

A: Given differential equation is: dydt+y=t2 The above equation is linear in y. The integrating factor…

Q: dV d(e") dy dy

A:

Q: dy 38. dt у сost

A: Given Information: The differential equation is dydt=ycost. Calculation: Calculate the general…

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: t sin (=) dt du

A:

Q: Find dx dy dy and dt' dt dx x = 9t – 9ln(t), y = 4t2 – 4t-2 dx dt dy dt dy dx

A:

Q: bx a a dy dx

A: Our Aim is to evaluate the integral given below:-∫0a∫0bxady dx -(i)

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.