1 If L{f(t)} 2e-4s determine f(t) 2s2 s(1 – e-4s)' -

Q: Q2. Solve the initial value problem 2- y = f(x) with initial condition y(0) = 2 and dx (0, 0<x<1…

A: Given differential equation is. dydx-y=fx                                      ........1 The given…

Q: Solve the follow ing initial value problem: 3x(t2- 1)dt+ (t³ + 8x- 3t)dx= 0, t(0)= 1

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Q: Solve the IVP d3 t3X(t) - 9x(t) = 18 e-3t dt x(0) =8 x'(0) = 9 x"(0) = 0 then find x(0.5) accurate…

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Q: Q3) Use Euler's method to estimate y(0.02) ey-x 1+ e2y y(0) = 1 ( h=0.01) .What is the error in the…

A: Given ; h = 0.01 y(0) = 1

Q: How do you solve question 8?

A: We use Newton Raphson method to solve the question listed. The formula is given as, The following…

Q: (b) Use the method of complementary functions and particular solutions, to determine the general…

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Q: Consider the following initial-value problem. f'(x) = 6x2 – 8x, f(3) = 21 Integrate the function…

A: Given: f'x=6x2-8x, f3=21   As we know the Power rule: ∫xndx=xn+1n+1+C

Q: Consider the following initial-value problem. f'(x) = 9x² – 10x, f(1) = 5 Integrate the function…

A: We have to find solution

Q: [  (1+ xsiny)dx - x2cosydy = 0  ] How can I find the solution "y" of this equation?

A: We shall use basic knowledge of first order ordinary differential equations to solve this question.…

Q: 1 Consider the function f(x) : 2x. At what value of T does f(x) 48 have a critical point? Round your…

A: The given function is: f(x)=148ex-2x For critical point, solve f'(x) = 0 for x.

Q: Solve the initial value problem given by y' = (x2 + 2y2)/(xy) ,  y(1) = 1 What is the interval of…

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Q: a) A capacitor (C) which is connected with a resistor (R) is being charged by supplying the constant…

A: Given : E = ∫0∞P(t) dt  ,   P(t) = 5Re-tRC2×R

Q: 1 1 ·dt /2x In(t + 1) g(x) =

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Q: 3.fCx)3D63X²4X+2 x<1 2x-1 X71 Part A: IS f(X) lontinuous ar X-1? JustfY answer. Palt…

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Q: 3. Obtain the Particular Solution when x = 4 and y = 1 (x+ y - 4)dx – (3x- y – 4)dy = 0

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Q: • Consider the (nonlinear) initial value problem =-2y. y(0) = 9% • Does it have a solution for a) 36…

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Q: Q5:al Using the Runge-Kutta method, solve x = 0.2 when h = 0.2. dy = x + y² with the initial…

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

Q: If the function f (x) solves the initial value problem dy = (x + 1)-1/2 – r dx - T. cos(T2) y(3) = 2…

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Q: 2xージ f (x) : 33 Vx2 T sin 2x + Ve2x + 2x –- In e, x # 1 1-x (1–3t)5(t³-8) g(t). t # 2 2-t

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Q: Obtain the particular solution satisfying the initial conditions indicated. 1. e* (3x°y-x)dx+e" dy =…

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

Q: 90% of it Suppose dy/dx = x-y and y = 2 when x 1, Use Euler's Method with increments of Ar = -0.1…

A: Given the differential      dydx=x-y with y(1)=2. Find y(0) using Euler's method with step size…

Q: Solve: x" -x+ 5 y'=t y" - 4y-2x = -2 with x(0) = y(0) = x'(0) = y'(0) = 0 Let L{x(t)} = U(s) &…

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Q: 5. The function h(x) = x² + bx² + d has a critical point at (4, -20). Determine the constants b and…

A: This question is related to the application of derivatives.

Q: How do I find the general solution of y''- 2y'= e^x * sinx using the method of variation of…

A: y''-2y'=ex sin x Auxiliary Equation: m2-2m=0⇒m1=0, m2=2 Complementary function  :  y=c1+c2e2xthis…

Q: Choose the solution value of x'' + w2x = fsinwt with initial conditions x(0) = 0 and x'(0) = 0

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Q: Find the function which solves the initial value problem dy/dx=2x−2, y(2)=−7 y(x)=?

A: The solution is:

Q: Please do show complete solution. m.) Find the critical point/s of the function f(x, y) = x³ + 2xy–…

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Q: 6. Using the u-substitution u = x2+ 1, solve the initial value problem dy 4.r Vr2 +1 and y(0) = 0 dr…

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Q: Solve the initial-value problem for y as a function of x. (16 – 2²) dy 1, y(0) = 7 dæ Y =

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Q: Find an explicit solution of the given initial-value problem. V1- dx - V1 - x² dy = 0, y(0) V1- V3x…

A: Given: The given equation is 1-y2dx-1-x2dy=0,y(0)=22

Q: (b) Evaluate (e) Given the function Rx) (x-2 + (y-3) O Find the critical points. (1)

A: The details calculation is given below

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: Find the general solution of y"-3 y'+2y = e2* [using variation of parameters] cos x

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Q: find the general solution of dy/dx + (3/x)y=2/x^2 as a function of x

A: Given,           dydx+3xy=2x2

Q: b) Use the initial condition y(0)= 2.14 to find the particular solution of -2y+x² + 2x* = 0 %3D dx

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Q: g(x,y)=y-x2=0 depending on the condition f(x,y) = x2+y2-6x+9   can you find with the lagrange method…

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Q: Use the method of variation of parameters to solve the initial value problem x' = Ax + f(t), x(a)=…

A: We have to find the solution x(t) using the method of variation of parameters.

Q: Use the method of variation of parameters to solve the initial value problem x' = Ax + f(t), x(a) =…

A: Given: A=9-33-1, ft =25t25t  , x0=00eAt =1+3t-9tt1-3tBy variation of parameters the required…

Q: 2 dt = (t – 5)°

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Q: 4. (a) dzy Solve: dx2 + ( = 0. (b) Solve xy" + (1 – x)y' – 2(1+x)y = e-*(1 – 6x) by the method based…

A: We have, d2ydx2+dydx+dydx3=0 ..i Put dydx=v ⇒d2ydx2=dvdx Now substitute in equation i we get…

Q: The

A: This is Linear Differential equation in x. We use method of separation of variables.

Q: If f(x, y) = -x - y* + 3xy - 2x - 5y, then in the process of obtaining its critical points the…

A: Introduction: The critical points of the two variables' function f(x,y) is given by solving the two…

Q: Use the method of variation of parameters to solve the initial value problem x' = Ax + f(t), x(a) =…

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Q: 3. Find the general solution of y"-3y'+2y = e* cos x [using variation of parameters]

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Q: d?x 4. Solve the IVP: dx 4. dt + 4x = t³e2t,x(0) = 0 ,x'(0) = 0 by any method - dt2

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Q: 16 Suppose we know that (3fx)-2)dr-6 4 and that Sxf (x²) dx =8. ise this information and properties…

A: We have to find ∫04fxdx

Q: If f(x, y) = −x2 + x3 - y + 4xy + y3, then in the process of obtaining its critical points the…

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Q: Use the method of variation of parameters to solve the initial value problem x' = Ax + f(t), x(a) =…

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