Q3\ Solve the problem minimize * J[y]= [[v +y"- 2y dx ,subject to the conditions y (0) =1 and y(1) = 0

Q: Q2: - If y = 3 sec3t and x = etan3t prove that: - dy (In3)² ,Y logy x %3D dx

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Q: Express the solutions of the initial value problems in terms of integrals. dy/dx = sec x, y(2) = 3

A: dydx   = Sec xdy  = Sec x dx Integrate both side

Q: Solve the initial value problem dx 2x cos(4t) - dt with x(0) = 1. x(t) = = sqrt(-1/4sin(4t)+1) Hint:…

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Q: Use Euler's method with step size 1 to estimate (¹), where y() is the solution of the problem y +…

A: Given that y'+3x2y=x2 Using Euler's method, find the value of  x at 1. Initial conditions are y0=3…

Q: 5. Find of the parameters: x = sin 2t and y = - cost at t = dx %3D

A: Topic = Derivative

Q: (1) Find the general solution for -) dx - -) dy = %3D

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Q: 3) Estimate Y(2) using Euler's method with 0.5 long dY intervals. Y - 2X and Y(1) = 0. dx

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Q: dx 5x cos(3t) dt with x(0) = -4.

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Q: Let y be the solution of the initial value problem y′′+y=−sin(2x), y(0)=0, y′(0)=0. Find the maximum…

A: Here, differential equation is y’’+y=-sin2x

Q: Find the value of X(0.3) for the initial-value problem dx dt = -xt, x(0)=1 using Euler's method with…

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Q: find dx/dt at x = 3 if y = -5x^2-4 and dy/dt = -3. dx/dt =

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Q: 2 max f (2х + и)dte dx - 5 — и?, x (0) 3D1,x(2) freet dt

A: Given: maxf=∫02(2x+u)dt dxdt=5-u2,     x(0)=1,      x(2).free

Q: 2. The rate at which the total average of COVID cases is dx increasing at x = 10 tents and 1 tent…

A: The solution are next step

Q: • Consider the (nonlinear) initial value problem / = -2y, y(0) = yo Does it have a solution for a)…

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Q: 28. Differentiate implicitly to find dy/dx if x + x/y = 7.

A: Given, x3+x/y=7 we can also write as yx3+x=7y,  or y=x7-x3 derivate both side w.r.t x…

Q: . Find P.S. of (16x +5y) dx + (3x+y) dy = 0 of the curre to pass thru the point (1,-3) 2. Find P.S.…

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Q: Suppose that glucose enters the bloodstream at the constant rate of r grams per minute while it is…

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Q: find dx/dt at x=1 if y=3x^2+3 and dy/dt=1

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Q: A clamped beam of length 3 is modeled by: y(4) = 24, y(0) = y'(0) = 0, y(3) = y'(3) = 0. Solve the…

A: The given differential equation is y4=24, with y0=y'0=0 and y3=y'3=0 Now we integrate the given…

Q: dy/(3x2) = (1 + y²)1.5 dx.

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Q: Solve the initial value problems for x as a functionof t. (3t4 + 4t2 + 1) dx/dt = 2√3, x(1) = -π√3/4

A: dxdt(3t4+4t2+1)=23=>dx=23dt3t4+4t2+1=>dx=23dt(t2+1)(3t2+1)=>dx=23…

Q: dx (2tx +x+ cos t) + (-sin x +t² +t)- = 0. dt %3D

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Q: 2 1 Estimate -dx using the right endpoint rule with n = 4 3 1+x

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Q: Find dy/dx at the given point. 7x2y4=9-x2-9y  at (0,1)

A: Given: 7x2y4=9-x2-9y We have to find the dydx at (0,1)

Q: 11.Solve dy - x+) y(2) = 2 by Fourth order Runge-Kutta Method at x = 2.5, and x = 3 %3D dx

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Q: Usually in a method of solution for Homogeneous DE, after the substitution of y = vx (or x = vy) and…

A: In the method of solution for homogeneous differential equation, The equation is of the form,…

Q: Determine the integrating factor xydy - (y2-3x2)dx = 0

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Q: Solve the initial value problem given by y' = (x − y)2 ,  y(0) = 0 What is the interval of…

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Q: y = x* Inx dy : =x³ +4x° Inx dx O Op tion 1 None of these dy - -x -4x° In x dx =x² -4x° Inx dx O…

A: Explanation of the answer is as follows

Q: solve the Initial Value Problem using Separation of Variables. y' = xy2, y(1) = 2

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Q: What is the value of the coefficient d of the equation y = ax + bx² + cx + d so that it will have…

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Q: 6. Why is it very easy to conclude that x2 dx diverges without making any integration calculations?

A: This question is taken from the calculus and sub-topic is improper integral in which we have to give…

Q: 1- (x²1) + dy 2xy = 1 ty Cosx Ex Sinh 2- Sin(x) dy dx 3- - dy dx + 3x²y = x²x³ + 4- xlnx dy dy +y =…

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

Q: Solve the differnetial equation: dy/dx=3/x^2-3x^2+2 with the initial conditions (1,8). show work

A: By using variable separable method we can calculate the given differential equation. See attached…

Q: 5. The integrating factor of the di equation 2y dx + (x- x^3 y^3) O x*3 y^2 O Does not exist

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Q: solve using homogenous and exact. (2x-3y)dx+(2y-3x)dy=0

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Q: Solve the initial value problem. nt 7y – 2y = e-, y(0) = Let a, be the value of a for which the…

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Q: 3/ Find Value of integral ) dx 0 X+1

A: I am attaching image so that you understand each and every step.

Q: 1-f²₁ ¹/²(y² sinx dx dy) 2-√²-dxx2 0 3- f(cscx cotx)² 2 4- f₁² x (x − 3)dx for 5-S²₂ (x³ + √x) dx

A: 1.

Q: A population x of rats satisfies the DE dx /dt ka?. Initially there are x(0) = 2 rats, and their…

A: The general solution of a differential equation always contains a constant of integration. The…

Q: dy Obtain general solution of- 3/xy dx

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Q: Solve the initial value problems for y as a functionof x. (x2 + 1)2 dy/dx = √x2 + 1, y(0) = 1

A: x2+12dydx=x2+1⇒dydx=x2+1x2+12⇒dydx=1x2+132⇒dy=1x2+132 dx Now integrating on both sides, we get…

Q: Let y be the solution of the initial value problem y" +y = - sin(2x), y (0) = 0, y'(0) = 0. The…

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Q: Find dx dt dx dt at x = = 2 if y= 2x² - 1 and dy dt - 3.

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Q: solve the Initial Value Problem using Separation of Variables. y' = cos2x, y(0) = π/4

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Q: Find the Bolution to the initial value problem. | -y = 2€ %3D %3D

A: Given IVPy'''-y'=2e-t+9e2t  ; y(0)=0 ,  y'(0)=-1   , y"(0)=2 to find the the general solution use…

Q: A cylindrical tank holds 22 liters of water. At time t = 0, two taps are opened simultaneously, the…

A: Please check step 2 for the solution.

Q: 2. ху 4 a. when x=8 10 dx b. when x-1 dt dy dt -6

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Q: (In x) dx Integrate: 1

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