Approximate the solution of dy _ y-1 dx x+3 with initial condition y(-1)=0 for –1

Q: equilibrium

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Q: Solve the inhomogeneous 1st order equation Ux − Ut = cost U(x, 0) = 0.

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Q: 2. Determine whether the functions f1(x) = e2", f2(x) = e=2#, and f3(x) = sinh 2x are linearly…

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Q: Solve the inhomogeneous 1st order equation U₂ - U₁ = cost U(x, 0) = 0.

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Q: Obtain two linearly independent solutions valid near x = 0 x2y" + x(x-1)y' + (1-x)y = 0

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Q: Show that the solution of the equation dx/dt=-x(k^2+x^2) With initial condition…

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Q: Given the Bernoulli's equation Dy/DX+yP(x)=y^n Q(x) and x=y^1-n, reduce the equation to the linear…

A: Given differential equation is                                           dydx+yP(x)=ynQ(x);  x=y1-n…

Q: Obtain a solution to x^2y"+xy'+(x^2-1/9)y=0 using the Frobenius method

A: We have to obtain a solution to x^ 2y^ prime prime + x * y' + (x ^ 2 - 1/9) * y = 0 using the…

Q: Question 2 Determine the general solution. x (dy/dx) = 2 - 4x^3. O y=lnx-(1/3) x^2 + c Oy=2…

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Q: Q9) Use the Rung-Kutta method to solve the following initial value problem: dy_(y-x²) =xe dx where…

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Q: Can you give the interval of the solution as a Bernoulli Equation?  y(0)=1 ie...  y'+p(x)y=g(x)y^n…

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Q: Find a particular solution y'''-y''-4y'+8y=6xe^2x

A: y'''-y''-4y'+8y=6xe^2x Particular integral = 6xe2x 6xe2xD3-D2-4D+8By using property shift F(D) to…

Q: Calculate dy/dx. You need not expand your answer. y =x2.3/9+2/x2.3)(9x − 1) Answer ----->dy/dx:…

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Q: Find the maximum of f(x) = 30x4 − 121x3 + 60x2 + 64x USING Newton’s method (x0 = 4, εs = 1%)

A: Given, fx=30x4-121x3+60x2+64x With initial point, x0=4 Differentiating the given equation up to…

Q: Let y(t) be the solution to y˙=5te^(-y)˙ satisfying y(0)=−3  (a) Use Euler's Method with time step…

A: Euler's method is a technique for numerical differentiation in which we compute the approximation of…

Q: Assume that  dx1/dt= x1(10-2x1-x2) dx2/dt= x2(10-x1-2x2) a) Graph the zero isoclines. b) Show…

A: Given- Assume that  dx1dt = x110 - 2x1 - x2dx2dt = x210 - x1 - 2x2 To find-  Graph the zero…

Q: Find two linearly independent solutions of 2x2y"-xy'+(-6x+1)y=0, x>0 of the form

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Q: mit equatio x²y' + 2xy + O with respect to x and solve for y'. Skip (you cannot come back) x²y + xy²…

A: Given query is to find the derivative.

Q: | 1) Find a function y whose graph passes through the point (1, ) and satisfies x²y' = y.

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Q: 2.Solve bernoulli (x ^ 2 + y ^ 2) * dx - xydy = 0

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Q: Q1: Solve the equation f (x ) = x e* -1=0 , by Bisection method where k=2.

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Q: [  y'''- y' = ex - 2x  ] Please find a particular solution yp for the above.

A: Particular Solution: Consider the equation Let be the differential operator Then equation (1) can…

Q: find the longest interval in which the following initial value problem is guaranteed to have a…

A: Consider the initial value problem    y"+P(x)y'+Q(x)y=g(x)y''(x0)=a                 y'(x0)=b If…

Q: Find an explicit solution for y′ = ye^−x^2 , y(0) = 1

A: The given differential equation is y'=ye-x2 and the initial condition is y(0)=1. Simplify the given…

Q: Solve the IVP dy r(x² + 1) 4y3 y(0) dr V2

A: We are given: dydx=xx2+14y3 ⇒4y3dy=x(x2+1)dx Now, Integrating both sides,…

Q: Solve dy/dx + 2y = 4, y(0) = 3 by one of the usual methods. Solve same the problem by Picard’s…

A: Integrating factor method for solving a differtial equation  Consider the differtial equation…

Q: compute (x2 - 8x +20) dx on the interval (0,1)

A: To evaluate the given definite integral over the open interval (0,1)

Q: Use the separation of variables to find the general solution to dy/dt = (3t + 2)*y^(4) Be sure to…

A: We have to find the general solution to the differential equationdydt=(3t+2).y4

Q: Example find y (1) if dy y (1) if dy = 1/(x-Y) ; Y(0) = 1 dx (Use h=1) using Eulers method and using…

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