Transform the equation rydx – (z+2) dy = 0 into the form of a %3D variable separable f(z) dz + g(y) dy = 0 O (e +2)dz z+2 # - *= 0 O z - ydy = 0

Q: please use laplace transform for the below linear system to solve system of equation. x(t)+6y'(t)=1…

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Q: Use the 4th order Runge Kutta method to integrate y'= 3.x²y using a step size of h = 0.1 and an…

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Q: Employ the fourth order Runge-Kutta method to integrate y' = 4e0.8t - 0.5 y from t=0 to 1 using a…

A: Using RK-4 method formula we can find the value of y(1) =6.201

Q: The solution of (1+y²) + (t- elan-ly Y =0 is: -1n dy %3D dt Select one: a. 1 t 3D elan-ly e2tan-ly O…

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Q: Exercise : 4 3 a) Evaluate , S /1-х2 |1-x²-y² .-3(x²+y²+z²)² dz dydx

A: Triple integral is used to find the volume bounded by a region. There are many methods that are used…

Q: Reduce the DE with linear coefficients (6x+ y-9)dx+ (x-2y+5)dy=0 to a homogeneous DE. (A (би + w)dw…

A: Given differential equation (6x+y-9) dx + (x-2y+5) dy = 0  .........(1)

Q: Apply Euler-Maruyama method as one step to solve the SDE 3 y dy dt + dB %3D 5 t y(1) = 2

A: Given: dy=3-y5-tdt+dBt y1=2 We have to apply Euler-Maruyama method as one step to solve the SDE.

Q: , 0 0 u(0,1) — 0, и(п,г) %3D0 sinx, u (х,0) — 0 Utt = Uxx, u(х,0) 3D

A: Consider the solution: ux, t=XxTt and the conditions are X0=0=Xπ, T0=fx=sinx and T'(0)=0  uxxx,…

Q: 7 Find the second linearly solution of the D.E x'y"+xy'-(x+2)y = 0, given that: y,(x) =

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Q: Find the general solution of dy – qy³ Py – dt by making a suitable substitution that transforms the…

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Q: Cons i der the linearsystem X2 1. 2. is Gauss-s eidel method

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Q: Find the general solution of dy -my – ny³ dt by making a suitable substitution that transforms the…

A: Differential equation

Q: ) y, = x2 IS ODE X²y"+2y-6y=0 SOLUTION OF THE USE THE REDUCTION OF ORDER FOAMULA TO FIND A SCCOND…

A: We have to use reduction formula:

Q: dz 또는 dt dw 1. 연쇄법칙을 사용하여 -를 구하여라. dt (1) z = xy + x² y, x =1+21, y =1-2 (2) z = /x²+y°, x = e', y=…

A: Given

Q: EXERCISE 1. dy ry+y Find the general solution of dr

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Q: Use Runge-Kutta method of order four with step-size h = 0.5 to approximate the solution for 2<t<3 of…

A: given IVP isdydt=-y+ty1/2y(2)=2h=0.5here dydt=f(t,y)where f(t,y)=-y+ty1/2t0=2y0=2h=0.5by using R.K…

Q: dy + 2y = 5t dt %3D For the initial condition y(1) = a, give the domain over which the solution is…

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Q: Consider the linear system : dx 2x – 2y %3D dt dy - 2x + y with initial conditions x(0) = 0 and y(0)…

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Q: 2. Show that the Euler-Cauchy Equation Iy" + axy + by = 0, 1+0 can be transformed into the constant…

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Q: Determine the critical points of the following system and analyse their stability: dz 1-zy, = dy…

A: As per the question we are given the following dynamic system : x' = 1 - xy y' = x - y3 And we have…

Q: Find the 23 dx dt general solution of the system = 3x -y-z dy = x + y - z dt dz = x-y+z dt

A: The given system of equation is  dxdt=3x-y-zdydt=x+y-zdzdt=x-y+z The objective is to find the…

Q: If x, y, and z are lengths of the edges of a rectangularbox, then the common length of the box’s…

A: Given- s=x2+y2+z2 To find- dsdt in terms of dydtand dzdt, if x is constant. Concept Used- As the…

Q: Let y(t) be the solution of (x3 + 1) dy dt = y satisfying y(0) = 1. Compute approximations to…

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Q: The homogeneous equation with constant coefficients of least order that has y = 2e3t + 3 sin(3t) +…

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Q: Apply Euler-Cauchy Runge-Kutta method for the equation: y' = 2y t y (1)=1 and and abtain y, Y₂ y h =…

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Q: dr = -4rt whent=0, r=r, dt Obtain the particular solution of - %3D

A: we have to use separation of variable

Q: Suppose that a projectile is fired straight upward from the surface of the earth with initial…

A: velocity v = rate of change of displacement y Hence, v = dy/dt Hence, d2y/dt2 = dv/dt = (dv/dy) x…

Q: Put the following initial value problem into a first order system form. (Show your workl) y(0) – 3y"…

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Q: Show that (0, 0) is an unstable critical point for the following system: 2xy + x3, 1 -x2 + y°. de dy…

A: We will find Jacobian matrix  for system of differential equation Then depend on eigen values of…

Q: (a) Show that V(x, y) = ln(1 + ²) + y² is a Lyapunov function for the system x' (t)= x(y-1), y(t)=-…

A: As per your query the solution of the part (a) of the problem 4 has been given in the next step.

Q: 6y" – 5y' + y = 0, y(0) = 4, y'(0) = 0

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Q: Compute the nonhomogeneous linear DE. a. y" -y = x + ex b. y"- 2y + y = x’e*

A: We are given Non homogeneous differential equation. We have to find their solution.

Q: -2x y' = y - x y'e* diferansiyel denkleminin genel çözümünü bulunuz.

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Q: The standard form of 3dy-xydx= 3y³e/3 by Bernoulli's ec 4x/3 dx 3 A dy ху = 3e**/3y3 dx 3 'x=…

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Q: The solution to the non-homogeneous DE y' - Бy +ву 3D2х + 3 is 2. a. Ae3x + Be3* +1/3 x + 7/9 b.…

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Q: What is the general solution to the follwoing equation: (4t+5y+4)dt-dy=0

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Q: Find the Wronskian of a given set {yı, y2} of solutions of 6. y"3(x21)y- 2y 0, given that W(T) = 0.

A: Given the differential equation and the value of the wronskian at pi as:

Q: Minimize F(y, u) = f¿u²(t) dt under ý = -2y + u with y(0) = 1, y(1) = 0. Is your solution unique?

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Q: dx dt dy dt = 1 6 (x−1)(5−x− 6y x ) = y 20(1− y x−1) Find the nullclines  of the system

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Q: Draw the slope fields of dy/dt = -t2y at integer values ( y is greater than or equal to -5 and less…

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Q: The general solution of 2y" -xy'+ (x - 24 ly = 0, is: OaC,xJ,) + C,xJ_(2) OcC,,(3) + C,xJ_(3x)…

A: The given equation is  x2y"-xy'+x2-24y=0                                  (1) The differential…

Q: Use Runge-Kutta method of order four with step-size h = 0.25 to approximate the solution for 2 st<3…

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Q: Find a general solution to (x' +xy')y' = y implict form F(x, y)= C : Give an

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Q: 4y" – y = 0, У-2) %3D 1, у(-2) %3D -1

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Q: a) Rewrite the given third order scalar initial value problem as y' = f(t, y), y(to) = Yo: (y')³…

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Q: Find the general solution of 0= -dy/dt -py-qy^5 by making a suitable substitution that transforms…

A: Given:- 0=-dy/dx-py-qy5 To find:- General solution of given differential equation

Q: If (х, у) %3D х" у"is an integratingfactor of the the DE. (1+ 3ху)dx + (ху-1 +x?)dy %3 0 Then, the…

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Q: The solution of (1 +y²) + (t – elan-lyay dt 0 is: Select one: a. t = ce2tan-ly+2 O b. -C elan-ly…

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Q: Find a fourth order homogeneous linear ODE with solution x(t) = 3t² – 1+6e¯4. -4t

A: The given solution is xt=3t2-1+6e-4t. We have to find a fourth order homogeneous linear ODE with the…