3. Solve the hypergeometic equation: (x2 -)y(3ax- 1/2)y+y = 0 as a series (a) in powers of x, and (b) in powers of (x-1).
-y-2x 2+2y de If - 1 + xy + y2 + x2 = 0 and it is known that day find all coordinate points on the curve where x = -1 and the line tangent to the curve is horizontal, or state that no such points exist.
Find the indicated coefficients of the power series solution about x=0 of the differential equation. (x^2+1)y''-xy'+y=0, y(0)=3, y'(0)=-6 (1 point) Find the indicated coefficients of the power series solution about 0 of the differential equation (x2 1)y ry y 0, (0) 3, y' (0) -6 r2 24+ r(9) (1 point) Find the indicated coefficients of the power series solution about 0 of the differential equation (x2 1)y ry y 0, (0) 3, y' (0) -6 r2 24+ r(9)
3. Consider the following ODE: (1 + 2%)/" - xy + y = 0 (a) Find the first 3 nonzero terms of the power series expansion (around x = 0) for the general solution. (b) Use the ratio test to determine the radius of convergence of the series. What can you say about the radius of convergence without solving the ODE? (c) Determine the solution that satisfies the initial conditions y(0) = 1 and (0) = 0.
1) Find two power series solutions of the differential equation (x² + 1)y" – xy' + y = 0 about the ordinary point x = 0. Hint: Check Examples 5 and 6 in 6.2 Example 6 Power Series Solution Solve (x + 1)," + xy - y = 0. Solution As we have already seen the given differential equation has singular points at = = ti, and so a power series solution centered at o will converge at least for...
0 14 + x2 2. (3 points) Solve the initial value problem xy'–3y = x?, y(i)=
☺ (x²+2)y" +3 xy'-y = 0 Sol. -te altex *-* = ! ----**-**+1 = "h For each differential equation find two lineavly independent solutious about the ordinary point power series X=0
solve the initial value problems by a power series (x-2)y’=xy, y(0)=4
Find partial differential z/partial differential x and partial differential z/partial differential y if z^2 +zx sin(xy)+ x^3y = 0 Find partial differential f/partial differential u, evaluated at the point where u = -1 and v= 1, if f(x, y) = x^3y, x(u, v) = v - u, and y(u, v) = u^2 +v^2
Q.3. The recurrence relation that leads to the series solutions of the differential equation y"- xy' + 2y = 0 is (n-2) Cn+2 (n+2)(n+1) n = 0, 1, 2, 3, ... Find the corresponding series solutions