Consider the differential equation 2y"' + 167" + 30y' = tan(x) Note that y = 1, y = e-3x, and y = e-5x are solutions of the complementary equation. Now consider using variation of parameters. Set up the expression for u,' in determinant form.
4. Find the solution to the differential equation y"+2y'+ 2y-S(t-) y(0) 0, y (0)-0 and graph it.
Find the basis function of the differential equation using Frobenius method 2ax(1 y (1-5x)-y = 0 2ax(1 y (1-5x)-y = 0
use the fact that y=x is a solution of the homogeneous equation x^2y''-2xy'+2y= 0 to completely solve thee differential equation x^2y''-2xy'+2y= x^2
One of the solutions to the following differential equation (1 – 2x – 2y + 2(1+x)y – 2y = 0 is known to be yı (x) = 1 +1 Find the second linearly independent solution y2 (2) using the method of Reduction of Order.
1. (x2-5x)y”-yʻ- y=0 Find the ordinary and singular points of the differential equation.
Problem #16: [2 marks] A solution, y = f(x), of the differential equation, x²y + 5x²y = xt has f(0) = }. What is f(1)? Problem #16: Enter your answer symbolically, as in these examples Save
3. Given the ordinary differential equation: (x-2y) dx And the initial condition y(0) = 1, approximatey(0.5) using the Heun method and step sizes of 0.25.
Consider the following differential equation. 4x^2y′′+3xy′+14x^2y=0 Consider the following differential equation. (c) Find the series solution (x> 0) corresponding to the larger root. 7.15 (8k1)2 !-9-17 (4k+1)2 (-1) 14* k19.17.(4k1)2 y(r) = x1/14 | 1 + y(x) = x1/4 | 1 + Σ k!.7.15-..(4k + 1 ) 2 に! Consider the following differential equation. (c) Find the series solution (x> 0) corresponding to the larger root. 7.15 (8k1)2 !-9-17 (4k+1)2 (-1) 14* k19.17.(4k1)2 y(r) = x1/14 | 1 + y(x)...
Solve differential equation 3x^2y" +6xy' +y = 0