Use Taylor's method of order two to approximate the solution of the following initial-value problem at t = 2: A y' = 4(t+y), 1≤t≤2, y(1)=0, with h = 를

Q: Find the general solution of x(x + 3)dy = 2dy + √(9- y²)(12x + 9 + 4x²) dx.

A: We will separate variables and then will integrate it to find general solution of given differential…

Q: Verify whether yı = 3t4 and y2 = 4 t-2 form a fundamental set of solutions for f y" +7t y' + 8 y =…

A: We will verify the given statement.

Q: 5. Use the method of variation of parameters to find the general solution to _y"—y'—2y=e³x.

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Q: b) Evaluate S(2y + 4z)dx + (2æ + 3z)dy + (4x + 3y)dz, where C is the curve given by r(t) = for 0 <t…

A: given ∫C2y+4zdx+2x+3zdy+4x+3ydz where C is the curve given by rt=t3,2sinπt2,3cosπt2 for 0≤t≤1…

Q: please use the method of variation of parameters to determine the particular solution y'"+30y"…

A: The given differential equation is:y'''+30y''-4000y=e-20x

Q: Given the initial condition y(0) : e–2y = y'? 3, what is the particular solution of the equation…

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Q: Let A = (²2²) 22 Find et and the general solution to X' = AX + (1)

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Q: Solve the following PDES by separation of variable metho (i): u +U, = 0 (ii): y'u, –x’u, = ди (iil)…

A: (i) uxx+uyy=0   ...i solve the PDE using separation  of varaible let u=XxYy differentiate with…

Q: Find the general and particular solution of the y"=3e³x if f(2)= k and f'(2)=k²

A: y"=3e³x if f(2)= k and f'(2)=k²

Q: For y''+3y'+2y=e^-x, use the variation of parameters formula to find a particular solution. Show…

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Q: if x(t) = tsin(3t) is a particular solution to the equation x" + qx = cost3t, then q = -9. Is that…

A: The given differential equation is: x''+qx= cos t (3t) From the hypothesis, x(t)=t sin (3t) is the…

Q: Solve the following equation y" + 2/ + y = * using the method of variation of parameters.

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Q: x' +(log3 3)x – v2 = 0

A: Note: If a polynomial gives one solution in complex number then conjugate of this solution must be…

Q: Solve the pollowing: () (^) 2+j =j(xtjy) X = ? y=? (1) (2+j)(3-j2) = a+jb () (x-j2y) -(y-j«)-2tj a:?…

A: (a). Given  2+j1-j = j(x+jy)⇒ 2+j1-j×1+j1+j = -y+jx⇒ 2+2j+j-11+1 = -y + jx⇒ 12+32j = -y + jxBy…

Q: Use variation of parameters to find a particular solution of the DE y/" – 4y + 4y then write down…

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Q: E.X; Let T = {E₁ = (-∞,a): a = R}U{R,Ø} be a topology on R and let A = [2,3), B=(3,4), C = (1,5], D…

A: It is given that,  T = Ea=-∞, a : a∈ℝ∪ℝ, ∅ is a topology on ℝ. We have to find the closure of the…

Q: Use the explicit Euler method to plot the  estimate y(2) if y(t) is the solution to y' = t - y3 with…

A: Given IVP is y'=t-y3, y(0)=1 we have  f(t,y)=t-y3 Here using n=10 steps, Then step size h=upper…

Q: Suppose that we need to find the solution of y" = y², y(a) = 0, y(b) = 2 by finite difference…

A: This question is about application of numbers theory

Q: Find a slope of the solution of y' = t – y at (3,1).

A: We have been given a linear differential equation dydt=t−y ______(i) (As y′=dydt)We have to find the…

Q: Show that the y = √x/₁/4(kx²/2) is a solution of y" + k²x²y=0_

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Q: For y(t) solution of y'=-4y(1-y/4)+3 find the intervals where the function of t is increasing or…

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Q: 2.ryy' = y? - 2x. Find the solution that passes through the point (1,2).

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Q: Is the equation y '(t) = 2y - t separable?

A: Given a differential equation, y't=2y-t

Q: What is the particular solution if y(1)=0? 1/2 xy = y + (x² + y³)"

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Q: Given equation is using Laplace 1- y" - 3y' + 2y = 4e²t y(0)= -3 & v'(0)= -5

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Q: Solve the Following First Order Linear Equation

A: The given differential equation is xy'-2x2y=ex2. Rewrite the above differential equation dividing…

Q: step-by-step for y'(1+2y)-2x=0, y(2)=0, and find the interval of validity of the solution clearly.

A: Given differential equation is                  dydx(1+2y)-2x=0      ⟹   (1+2y)dy=2xdx Intergrating…

Q: differentiate the following: Q(y)= y3/3 + 3/y3

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Q: 8. (a) For f(x) = Vx, give the linearization at a = 25. (b) Use your answer from part a to approxi-…

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Q: Solve the given differnetial equation by undetermiend coefficents  y'' + 2y' = 2x +7 -e-2x   y(x)…

A: Given:-           The differential equation  is:…

Q: h(x) = px³ + 4px + 1, where p and q are constants. Given that h(-1)=-41 and h'(-1)=67, find the…

A: h( x ) = px3 + 4px + qxh( -1 ) = -41 h'( -1 ) = 67