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In Problem 1 –6 , classify the critical point at the origin of the given linear system.
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Fundamentals of Differential Equations and Boundary Value Problems
- Obtain two linearly independent solutions valid near x = 0 x(1 - x)y" - 3y' + 2y = 0arrow_forwardFind the general solution of the given system. dx/dt=3x-y dy/dt=9x-3yarrow_forwardconsider the nonlinear second-order ODE x''+2x'+4x/(1+x^2)=0 a. convert to DE to a system b. Find all critical points of the resulting systemarrow_forward
- EXAMPLE 4 Find the trajectories of the system (22) dxdt=4−2y,dydt=12−3x2.arrow_forwardConsider the systemdx/dt = 2dydt = y^2. (a) Calculate the general solution for the system.(b) What solutions go to infinity?(c) What solutions blow up in finite time?arrow_forwardFind the general solution of the given system. dx/dt = 4x-y dy/dt = 16x-4yarrow_forward
- Show that the relation y^2 - x^3 + 8 = 0 implicitly defines a solution to the nonlinear equation dy/dx = 3x^2/2y.arrow_forwardShow that the equation x2 + y2 = 2003 has no solutions in theintegers.arrow_forwardPart 1 of 3 Find a solution to the system[x'y']=[−62−2−10] [xy][x′y′]=[-62-2-10] [xy]by solving the IVP with initial condition [x(0)y(0)]=[1−4][x(0)y(0)]=[1-4] →x(t)=x→(t)= exp(t) ++ t exp(t)arrow_forward
- Consider the equation system: y2 + w2 − 2xz = 0 x3 + y3 − z3 + w3 = 0 Prove that exists surrounding neighbourhood of point P = (1, −1, 1, 1) in which the solution (x, y, z, w) can be written with x and z as functions of (y, w)arrow_forwardYou are given the following inhomogeneous system of first-order differentialequations for x(t) and y(t) in matrix form: x ̇ = 2x + y + 3 et ,y ̇ = 4x − y Write down the general solution of the original inhomogeneous systemarrow_forwardInvestigate the type of critical point (0,0) of the given linear system. dx/dt = -6x+13y+x^3 dy/dt = -x-2y+y^4arrow_forward
- Linear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage Learning