Question: how i can dsolve this differential equations.....

hi...

how i can dsolve this differential equations and obtain w(x) and U(x) and phi(x) analytical or numerically?

thanks

zah.mw
 

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restart; L := 100; h := 1; eq1 := 1130*(diff(U(x), x, x))+1130*(diff(W(x), x))*(diff(W(x), x, x))+1130*(diff(U(x), x, x, x, x))

1130*(diff(diff(U(x), x), x))+1130*(diff(W(x), x))*(diff(diff(W(x), x), x))+1130*(diff(diff(diff(diff(U(x), x), x), x), x))

(1)

eq2 := 1130*(diff(W(x), x))*(diff(U(x), x, x)+(diff(W(x), x))*(diff(W(x), x, x)))+(diff(W(x), x, x))*(1130*(diff(U(x), x))+565*(diff(W(x), x))^2-2.2*(int(diff(varphi(z), z), z = -5/2 .. 5/2)))+(14125/6)*(diff(W(x), x, x, x, x, x, x))+(10405/6)*(diff(W(x), x, x, x, x))+10

1130*(diff(W(x), x))*(diff(diff(U(x), x), x)+(diff(W(x), x))*(diff(diff(W(x), x), x)))+(diff(diff(W(x), x), x))*(1130*(diff(U(x), x))+565*(diff(W(x), x))^2-2.2*(int(diff(varphi(z), z), z = -5/2 .. 5/2)))+(14125/6)*(diff(diff(diff(diff(diff(diff(W(x), x), x), x), x), x), x))+(10405/6)*(diff(diff(diff(diff(W(x), x), x), x), x))+10

(2)

eq3 := diff(varphi(z), z, z)-.35*(diff(W(x), x, x))

diff(diff(varphi(z), z), z)-.35*(diff(diff(W(x), x), x))

(3)

dsys3 := {eq1, eq2, eq3, U(0) = 0, U(L) = 0, W(0) = 0, W(L) = 0, `ϕ`(-(1/2)*h) = 0, `ϕ`(-(1/2)*h) = 2, ((D@@1)(W))(0) = 0, ((D@@1)(W))(L) = 0, ((D@@2)(W))(0) = 0, ((D@@2)(W))(L) = 0}; dsol5 := dsolve(dsys3, 'maxmesh' = 1200, numeric, abserr = .1, output = array([.5]))

Error, (in dsolve/numeric/process_input) input system must be an ODE system, got independent variables {x, z}

 

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