Question

solve (2x-1)²d²y/dx²+(2x-1)dy/dx-2y=8x²-2x+3​

Answer 1

Answer:

On dividing the given equation by x^2, it becomes y'' - 2[(1+x)/x]y' + 2(1+x)y/x^2 = x, which is a second order linear differential equation of the form : y''+f(x)y'+g(x)y = r(x), where x.f(x) and (x^2).g((x) and r(x) are analytic at x=0, i.e. x=0, is a regular singular point of the equation. Accordingly we apply the Frobenius' Extended Power series method and put

y=Sigma(n=0 to inf.)(c_n)x^(n+k), in the original equation, where the coefficients c_n and the index k are to be determined by differentiating the above, twice with respect to x and by comparison of coefficients of x on the two sides of the equation

EAGERLY WAITING FOR THE BRAIENLIST CHOSSING

Answer 2

Step-by-step explanation:

let z=log(2x-1)

from here e^z=2x-1

x=e^z+1/2

(2x-1)^2d^2