Find the particular solution to: dy 2e2t – e-t given that y = 2.5 when t= ln 2 dt

Q: dy for each of the following: (2 p dx 5. Find (a) y=|(cost+e' – sint+3t³ )dt 3. csin x (b) y = (t2 +…

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Q: . solve for y(3) at h =1.5, given y(0)=5 using heun’s equation and euler’s method dy dx = 3e −x −…

A: Heun's method: Heun's method also known as Euler's modified method. It works in following steps. 1.…

Q: 10. Find * 10 S° S? er dx dy •5 2e25 + 1 S + 1 e25 + 1 e25 – 1 O e25 - 1

A: We will find given integral by changing order of integration. we will use following integration…

Q: If x= sint and y = cost then 2 dx dy dt dt O 2 O -1 O 1 O O O None of these

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Q: 20. Evaluate dædy by changing the limits of integration appropriately. e y/2

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Q: Show that y(t) =t-2 ln t is a solution to ty"+5ty' +4y 0. (where t> 0)

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Q: Solve the initial value problem dy (x? + 4) + 3xy = x, y(0) = 1. dx %3D

A: Consider the initial value problem x2+4dydx+3xy=x,      y(0)=1

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

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

Q: Solve the following initial value problem for y as a function of x dy 3+ /39 Vx² - 2- 25 = 1, x> 5,…

A: Here we have to use the following formula 1)  ∫dxx2-25=ln x+x2-25+c2)  lnab=ln(a)-ln(b)

Q: Solve (1+x ) = x²y, given that x=1 when y = 2 dx Find the particular solution for y in terms of x.…

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Q: dy dt y = (t tant) ¹ Find 11

A: y= (t tant)11 y= t11 tan11tUsing formula ( d(uv) = uv'+vu' )diff w.r.t "t"dydt=t11.11tan10(t) sec2t…

Q: e the differential equation by th 1. dy_ x + y dx 2. – a² .2 dy y? – x?

A: Multiple questions:Since you have asked multiple questions, we will solve the first question for…

Q: dy Find dx y = 5 In x + 2 log 5× dy (Type an exact answer.) %3D dx

A: Explanation of the answer is as follows

Q: d Q. S Vt In(t)dt equals dx a. 4x³ (In x) – /2 ln(2) b. 4x5 (ln x) – /2 ln(2) c.4x³ (ln x) d. 16x°…

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Q: S e6m sin m dm Integration by Parts

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Q: Given the equation dy = 3x2 +1 with y (1) = 2 %3D dx Estimate y(2) by Euler's Method using h = 0.5…

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Q: The quantity of a substance can be modeled by the function N(t) that satisfies the differential…

A: We have to find the quantity of substance at t=1.8.

Q: Solve the following differantial equation using finite difference method. d²x(t) + di? dx x(1) = 0…

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Q: d etermine whether or not diffential eq is exact (1/x^2 - 1/y^2)dx + (2x+1 / y^3)dy=0 if exact solve

A: given differential equation is  (1x2-1y2)dx+(2x+1y3)dy=0

Q: dy Solve the initial-value problem for y as a function of x. (49 – x²). dx = 1, y(0) = 4 Y =

A: We will solve this integration using trigonometric substitution as follows

Q: dy = ( e )dx

A: See the attachment

Q: (e*+ Y + ye") dx + (xe" – 1) dy = 0, y(0) = -1 %3D

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Q: Dse Runge - kutta method to Solve the equation: dly x +y %3D dx at x =0.8 given that using h= o.4 y…

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Q: 1. Solve for y3 using the method of successive approximation. dy = x + y; y(1) = 1 dx

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Q: dy The degree of the differential equation e dæ5 sin x is not defined O 5 O 1 O 2

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Q: Q1: Find dy/dx of the following functions: 1. x'e? y = log2 2Vx +1 2. (x - 2)*VI+5 y = Vx +4 y = t…

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Q: use Euler’s Method to approximate the given value of y(t) with the time step h indicated. y(3.3);…

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Q: 2 y +-y=D = 2t³ In(t), t> 0. (a) Verify that y = t*(1 – 2 ln(t)) is a solution of (1)

A: Take y, differentiate and substitute everything in equation (1).

Q: d Q. A Vi In(t)dt equals dx a.36x6 (In æ) – V2 In(2) b. Vr6 ln(x°) – V36 In(3®) 6x² с. 6а? (In x)…

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Q: Integrate the following differential and determine the constant of integration: dy/dx = 8/x which…

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Q: Determine the difference approximation of the problem d dy] (1+ x?). - y = x² + 1, y(-1) = y(1) = 1…

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Q: Q2: Suppose the electric potential at (x, y) is given by f(x, y) = 0.5 Ln(x² + y²) estimate the…

A: In this question, we have to find the error in f(x,y) and percent relative error for the given value…

Q: Consider the function Z = 2x²(1 – e-) where x and y are given to be 5 and In 5 respectively. Find…

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Q: d Q. A Vē In(t)dt equals dx a.36x6 (In x) – /2 1n(2) b. V#6 In(x®) – V36 In(3®) с. 6х? (In a) d.36x"…

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Q: Zy dx = (x?-1)L dx-dy) %3D

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Q: dy for e dx (*² +1), 6. Determine ln( 19) + x² – xy =

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Q: dy A: Compute dx at the point (1, 0) for the function y = cot-1(4x + eln(sin2x)) + sinh(3) + log2 x²…

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Q: Q5; Use three iteration of Picard's method to solve dy = 3x+ y when x=0.1, given that y 1 dx for…

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Q: (e^x+lny+(y/x))dx+(x/y+lnx+siny)dy=0 solve using exact equation (diff eq)

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Q: dy 1+y3 Determine the solution for the given DE: + = 0 dx xy?(1+x²)

A: Proceed as shown below

Q: OBTAIN THE GENERAL SOLUTION 2. dx: t (1+e?) see" x dt 3. x dx - Ja - x² dy =0

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Q: dx Given y= e-2x? dy when X = 1 and dt 2. Determine the value of dt

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Q: An object moves in one dimension with avelocity in m/s given by v(t) = 8 sin ∏t + 2t. Find its…

A: Given: The velocity of an object in m/s is given by  v(t)=8sinπt+2t Time interval is t=0 to t=10

Q: * = k (T – Tm) dt where T To

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Q: d²y The degree of the the differential equation dx? dy =y is 2 dx Select one: True False

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Q: dx = x – y – 2 cos(t) dt dy = x + y + 5 sin(t) dt Suppose you want to solve by substitution, Pick…

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Q: Let @ = 7e* dx ^ dy + ae³ dx ^ dz and n = 7e*y dx + 14e* dy+ e³ dz, where a E R. Find the value of a…

A: Given: 2-form, ω=7exdx∧dy+αeydx∧dz. 1-form, η=7exydx+14exdy+eydz.  where α∈ℝ. To find: The value…

Q: dy What value of k would make the differential equation + In(x + 1) x°yk variables separable? dz

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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.