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27. Consider the Euler equation xạy" + a xy' + By = 0. Find conditions on...
Consider the differential equation: xạy" + 15xy' + 48y = 0. Find all values of r such that y=r" satisfies the differential equation for x > 0. If there is more than one correct answer, enter your answers as a comma separated list. r=
2) Obtain a solution for the following: a) xạy” – 4y = 0 b)xy” + y + xy = 0 c) xy” – (x+1)y' - y = 0
Find all solutions to the equation x' +27 = 0 over the Complex Numbers. Do all parts (a)-(d): (a) Graph complex number -27+0.i as a vector in trigonometric form (b) Use De Moivre's Theorem to find one cube root of -27 (c) Graph all three solutions as vectors (in trigonometric form) on the xy-plane (d) Lastly, convert each solution from trigonometric form reise to standard form a +bi
Find all solutions to the equation x' +27 = 0 over the Complex Numbers. Do all parts (a)-(d): (a) Graph complex number -27+0.i as a vector in trigonometric form (b) Use De Moivre's Theorem to find one cube root of -27 (c) Graph all three solutions as vectors (in trigonometric form) on the xy-plane (d) Lastly, convert each solution from trigonometric form reise to standard form a +bi
3. Find all critical points of dt dt with the constraint PP = 8 0 (c and boundary conditions x(0) - 0, x(1)- 3. Hint: Write the Euler Lagrange equation (there is no dependence on t), and then use the boundary conditions and the constraint to reach a system of 2 equations (with quadratic terms) of two unknown constants a, b Solve it by first finding a quadratic equation for a/b 3. Find all critical points of dt dt with...
1. Consider the problem x' (t) = (1+t)x(t), x(0) = 5 (a) Find the Picard iterates xi(t) and x2(t). (b) Find the first two approximate solutions x, and x2 in the Euler scheme. (c) Find the exact solution. 2. For which initial conditions will the solution of x"(t) + 4x'(t) - 20x(t) = 0 tend to zero t → 00?
can I get details pls Find all solutions to the equation x' +27 = 0 over the Complex Numbers. Do all parts (a)-(d): (a) Graph complex number -27+0.i as a vector in trigonometric form (b) Use De Moivre's Theorem to find one cube root of -27 (c) Graph all three solutions as vectors (in trigonometric form) on the xy-plane (d) Lastly, convert each solution from trigonometric form reise to standard form a +bi
Consider the equation 3x²y" + x(2 – xy + xy = 0 with regular singular point Xo = 0. (a) Find the indicial roots ri, r2, with ri r2. Show your calculations. (b) Which of the following is true for the equation above: Indicate the letter of your choice and explain your choice. % There are two linearly independent convergent series solutions of the form yı (x) = x Š cux" and y(x) = x Š b,x". H0 N=0 (1)...
4. (a) Find and write down the general solution of the ODE 2y" – xạy=0 in the form of a power series about x = 0. Only include the first three non-zero terms in each of the two linearly independent solutions in an interval I centered at x = 0) that you obtain. (b) Check that each of the two linearly independent solutions you found in part (a) individually satisfies the ODE, up through terms of order x12.
MATLAB HELP 3. Consider the equation y′ = y2 − 3x, where y(0) = 1. USE THE EULER AND RUNGE-KUTTA APPROXIMATION SCRIPTS PROVIDED IN THE PICTURES a. Use a Euler approximation with a step size of 0.25 to approximate y(2). b. Use a Runge-Kutta approximation with a step size of 0.25 to approximate y(2). c. Graph both approximation functions in the same window as a slope field for the differential equation. d. Find a formula for the actual solution (not...