Differential Equations Answers

Solve the Bessel's equation of order zero

y^''(x)+(1/x)y^'(x)+y(x)=0

With boundary conditions y^'(0)=0, y(1)=1

Solve the following non-homogeneous linear ODE of first order

dy/dx + 3y/x =6x^2

Solve by finding an integrating factor

(x^2+y^2+2x)dx + 2ydy =0

Find the equation of the elastic curve and its maximum deflection for the horizontal, simply supported,

uniform beam of length 2l metres, having uniformly distributed load w kg/metre.

y" - y = e2x[3 tan e+ 3 (sec e)^2]

Differentiate with respect to x

f(x) = 6x

y = 12e^5x

y = ln3x

Solve the differential equation by an appropriate method. y''+2y'=x^2+4e^2x

solve the differential equation dy/dx + (x/1-x^2)y=xy^1/2 , y(0)=1

solve the differential equation dy/dx +(x/1-x^2)y=xy^1/2 , y(0)=1

Use the Laplace transform to solve the given initial-value problem.

y'' + 5y' + 4y = 0,    y(0) = 1,  y'(0) = 0

y(t) =