Differential Equations Answers

Find the eigenvalues and associated eigenfunctions of the
Strum-Liouville problem: xy''+y'+(λ/x)y=0
y'(1)=0,y'(e^(2π))=0.

put the following equation into sturm-liouville form x^2y^''+xy^'+(λx^2-n^2)y=0

Solve the boundary value problem:
∂u/∂t = β(∂^2u/∂x^2), 0 < x < L, t > 0
u(0, t) = 0, u(L, t) = 0, t > 0
u(x, 0) = f(x) 0 < x < L

Solve the differential equation.
(D²+D+D')z=0

Solve the Lagrange's equation (1-x^2)y"-2xy'+n(n+1)y=0

Solve the initial value Problem
dN/dt = τ (N − N^2/q) N(0) = No, where τ, q are positive. Hence or otherwise, find the solution of the Verhulst model
when t → ∞

Find the Wronskian of a given set {y1, y2} of solutions of
(1 − x^2)y" − 2xy' + α(α + 1)y = 0 when W(0) = 1

Solve y^2dx-z dy+dz=0 equation for
Exact differential equation Method

Solve the PDE
(x+2z)p+(4zx-y)q=2x² +y