(1) (a) Find the derivatives of functions f(x) = e2 and g(x) = 5æ?. (b) Compute the definite integral e2a + 2xdx

Q: Solve the differential equation dx/dt = 1 - t +x -tx for x(-1) = -2

A: Given : dxdt = 1 - t + x  - txx-1 = -2

Q: Obtain the differential equation associated with the given function: y = Cx² + c2.

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Q: 4. What is the differential equation of the given functions? • y = Ce-* + Cze-2x + x y = Ce2* +…

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Q: Solve the differential equation for y in terms of x 1) y' + xy = 2x

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Q: x-1, X)1 find the generol solution of the differential eguation below

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Q: Solve the differential equation. cos x dy/dx + y sin x = sin x cos x

A: Simplify: Divide by cos xdydx+ysin xcos x=sin x cos xcos xdydx+y tanx=sin x

Q: y = Ce * + C2e 2x + C3e * + e 2x

A: y=c1e-x+c2e-2x+c3e-x+e2xy=c1+c3e-x+c2e-2x+e2x Here, complimentary solution is  y=c1+c3e-x+c2e-2x…

Q: Solve the differential equation of the given function by elimination of arbitrary constants y =…

A: we  need to find the differential equation for the given solution by elimination of arbitrary…

Q: Given the differential equation: D'(sin x- cos x+3e" +x) What is the second derivative? a - sin…

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Q: Solve the differential equation. y'+y tan x = cos x, - n/2 < x < r/2 A y = x sin x + c cos x, - 12…

A: Consider the given linear differential equation which is required to solve. Comparing the above…

Q: 3. Solve the differential equation y' - 2ty = t by multiplying both sides by an appropriate…

A: Given differential equation:-    y' - 2ty = t

Q: find the differential equation for the family of circles (x- A )*+ ly- B)' = A

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Q: Solve the differential equation using series: (x + 1)y'' - (2 - x)y' + y = 0.  where y(0) = 2 and…

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Q: where y is considered to be a function of . In this exercise, you will determine whether or not y =…

A: The given differential equation is y' = y2. The objective is to determine whether the equation y =…

Q: (ii) Show that the differential equation is not exact. (2y² + 3x) dx + 2xydy = 0

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Q: 1) y"+ y – 2y = e" + 4 sin x + x² – x solve this differential equation from derivative operator.

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Q: Given a differential equation (3x²y + 2xy + y³) dx + (x² + y²) dy = 0. What is the Integrating…

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Q: The Bernoulli's form of the differential equation x²dy+ (2xy-y³dx=0 is The Bernoulli's form of the…

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Q: (a) Solve the first order linear ordinary differential equation dy x sin x- + (sin x + x cos x) y =…

A: The solution is given as

Q: Show proof that this equation is an exact differential: (y + z)dx + xdy + xdz

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Q: prove that the function f(x) = e¯* sin(x) satisfies the е differential equation ƒ (x) + ƒ'(x) = e¯ª…

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Q: 5. Check whether following is homogenous differential equation, (x-2y)dx+xdy=0 and also solve it.

A: Given: The differential equation is (x-2y)dx+xdy=0. To check: The given equation is a homogenous…

Q: Solve the exact differential equation ( - 2 sin(x) – y sin(x) + 4 cos(x))dx + (cos(x))dy = 0 where…

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Q: 1. Discuss in detail the connections between differential and integral calculus.

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Q: Solve the differential equation: (2xy-sinx)dx+(x² - cosy)dy=0.

A: The given differential equation is  (2xy-sinx)dx+(x2-cosy)dy=0 It is of the form , Mdx+Ndy=0 . This…

Q: Given the differential equation: D°(sin x-cosx+3e* +x) 1. What is the second derivative? a - sin…

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Q: A function x(t) satisfies the differential equation dx –xª – 7x³ + 18x² - dt

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Q: 2. The exact differential d xdy - ydx what is the d(xe")= x?

A: Let's find.

Q: Determine the function f satisfying the differential equation f'(x) = xe-f(x) and f(0) = ln(2) =…

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Q: 4. Find the differential equation of a family of circles, each having its center on the line y = x…

A: To find the differential equation of a family of circles, each having its center on the line y=x,…

Q: 38. Determine the integrating factor of the linear differential equation y' - (1 + tanx)y = e cos'x.…

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Q: Find the differential coefficient f’(x) of the following implicit function:         x3 - y3 + 2x =…

A: To Find the differential coefficient f’(x) of the following implicit function:         x3 - y3 + 2x…

Q: (5) Solve the differential equation by variable separable x² tan ydy = (x²e" ln x + xe®)dx %3D

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Q: Example 11 : Find the equation of the curve satisfying the differential eguatio- dy (1+x?)+2xy= 4x²…

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Q: dy + ydx = 3x²y?dx, %3D

A: Let's find.

Q: Find the differential equation of the primitive x = A.sin (y + B)

A: We need to find the differential equation of the primitive x=Asiny+B  Basically we need to…

Q: Given the differential equation: D´(sin x- cos x+ 3e* +x²) What is the fourth derivative? a - sin…

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Q: Solve the differential equation 3y + 3y (sin-¹x)√1-x² : 1

A: The given differential equation is 3y'+3ysin-1x1-x2=1.

Q: Given the differential equation: D'(sin x- cos x+ 3e +x) What is the second derivative? – sin…

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Q: Consider the following differential equation. (x2 + y2)y′ = y2 Let  f(x, y) =  y2/x2 + y2 .  Find…

A: This is a problem of differentiation of the function. Based on the general formula we will answer…

Q: (a) Solve the homogenous ordinary differential equation: dy у (x — у) dx x2

A: Substitute y= vx to solve the given problem.

Q: Demonstrate that the function f(x)= e^-x sin (x) is a solution for the differential equation f(x) +…

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Q: Obtain the differential equation associated with the given function: y = Cx² + C².

A: first we will derivative with restive x then find the value of C then put in given equation

Q: Q-21 Solve the linear Differential dy + (x sin x + cos x)y = 2 dx equation x cos x-

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Q: Obtain the differential equation of the strophoids y2 = x²(a+x) a-x

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Q: (D² + 4) y = tan 2x

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Q: - Find the differential equation associated to the equation: y=C₁e sin x + C₂e cos x

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Q: Solve the differential equation: (D² + 1)y = tan x

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Q: 2. Solve the differential equation dy 2y-cot x tan dx

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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.