MATLAB: 4th order differential equation

differential equations

Hello, Can anyone help me with solving below?

EI(d^4v/dx^4) = w

Boundary conditions are

v(x=0) = 0 ; v(x=L)= 0; dv/dx(x=0) = 0 ; dv/dx(x=L) = 0

Best Answer

syms y(x) w EI L
c1=y(0)==0
y1 = diff(y,x)
c2=y1(0)==0 
c3=y(L)==0
c4=y1(L)==0
y(x)=dsolve(diff(y,x,4)==w/EI,c1,c2,c3,c4)

Related Solutions

MATLAB: How to solve a boundary value problem (differential equations) which contains dependent variable values at the boundary??? The equation is like a integro-differential equation.

Try "dsolve" on the problem

(-iy+y'''')=(A+Bx)*C2+(C+Dx)*C1

with boundary conditions

y(0)=0, y'(0)=1, y''(1)=0, y'''(1)=0, y''(0)=C1, y'''(0)=C2.

Best wishes

Torsten.

MATLAB: How to solve this question? And the ODE equation made me confused.

See bvp4c() for boundary condition problems. Something like this

EI = 1.3e7;
q0 = 30e3;
T = 20e3;
L = 4;
xmesh = linspace(0, L, 100);
odeFun = @(x, y) [y(2);
                  1./EI*(1+y(2).^2).^(3/2)*(1/6*q0*(L*x-x.^3/L)+T*y(1))];
              
bcFun = @(yl, yr) [yl(1)-0;  % y(0) = 0
                   yr(1)-0]; % y(L) = 0;
               
guess = bvpinit(xmesh, [0; 0]);
    
y_sol = bvp4c(odeFun, bcFun, guess);
plot(y_sol.x, y_sol.y);
legend({'$y$', '$\dot{y}$'}, 'Location', 'best', 'FontSize', 16, 'Interpreter', 'latex');

Best Answer

Related Solutions

MATLAB: How to solve a boundary value problem (differential equations) which contains dependent variable values at the boundary??? The equation is like a integro-differential equation.

MATLAB: How to solve this question? And the ODE equation made me confused.

Related Question