(1 point) 6y 6xe-6x, 0 < x < 1 with initial condition y(0) = 2. Given...
Consider the following. x' = 6x − 10y y' = 10x − 6y, X(0) = (6, 10) (a) Find the general solution. (x(t), y(t)) = Determine whether there are periodic solutions. (If there are periodic solutions, enter the period. If not, enter NONE.) (b) Find the solution satisfying the given initial condition. (x(t), y(t)) = (c) With the aid of a calculator or a CAS graph the solution in part (b) and indicate the direction in which the curve is...
2. -13 points ZillDiffEQModAp111.1.011. 0/6 Submissions Used My Notes Verify that the indicated function is an explicit solution of the given differential equation. Assume an appropriate intervall of definition for the solution. 6y + y = 0; y = e-x/6 When y = e-x/6 y'a Thus, in terms of x, 6y' + y = 3. -12 points ZillDiffEQModAp111.2.001. 0/6 Submissions Used My Notes Ask Your Teacher In this problem, y = 1/(1+ce) is a one-parameter family of solutions of the...
Solve the given differential equation with initial condition. y'-6y = 0, y(0) = 9 The solution is y(t) = (Type an exact answer.)
5. Find a solution of a IVP consisting of the DE y-2 y=cie 3 6x+4, with solution 33 + coe-2x and initial conditions 1(1) 4, y'(1)-2 6. Given a direction field, sketch by hand an approximate solution curve that passes through a given initial condition (a) y(0) 0 (b) y(0) 2 5. Find a solution of a IVP consisting of the DE y-2 y=cie 3 6x+4, with solution 33 + coe-2x and initial conditions 1(1) 4, y'(1)-2 6. Given a...
1 point) An equation in the form y + p(x)y -(x)y with n 0, 1 is called a Bernoulli equation and it can be solved using the substitution wich transforms the Bernoulli equation into the following first order linear equation for v: Given the Bernoulli equation we have n- We obtain the equation u' Solving the resulting first order linear equation for v we obtain the general solution (with arbitrary constant C) given by Then transforming back into the variables...
7. (10 points) Find the explicit solution to 1 94" + 6y' + y = 0 with initial condition y(0) = and y'(0) = -2
(1 point) Solve the Bernoulli initial value problem - 2 'y', y(1)=2 For this example we haven We obtain the equation + given by Solving the resulting first order linear equation for u we obtain the general solution with arbitrary constant Then transforming back into the variables 2 and y and using the initial condition to find C Finally we obtain the explicit solution of the initial value problem as
1 point) Given that y -x is a solution of dy dx2 in x > 0, find another solution yc of ус the same equation such that (xy.) is a fundamental set of solutions
A first order linear equation in the form y p(x)y = f(x) can be solved by finding an integrating factor u(x) = exp c) dx (1) Given the equation y 2xy = 10x find H(x) = (2) Then find an explicit general solution with arbitrary constant C у %3 (3) Then solve the initial value problem with y(0) = 3 A first order linear equation in the form y p(x)y = f(x) can be solved by finding an integrating factor...
y = 1/(x2 + c) is a one-parameter family of solutions of the first-order DE y' + 2xy2 = 0. Find a solution of the first-order IVP consisting of this differential equation and the given initial condition. y(-3) = y = Find the domain of y considered as a function over the reals. (Enter your answer using interval notation.) Give the largest interval I over which the solution is defined for the given initial condition. (Enter your answer using interval...