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Question: factor differential operators

Question:factor differential operators

mehdi jafari 769 Maple
factorization differential-equations dfactor
September 08 2021
1

i have two equations;i.g eq1 and eq2. i want to factor psi(x,t) in eq2 using linear differential operators and substitute it in equation 1. could anyone help?


 

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restart:with(DEtools):
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eq1:=E*D(II)(x)*D[1](psi)(x,t)+E*II(x)*(D[1]@@2)(psi)(x,t)-G*A(x)*psi(x,t)+G*A(x)*D[1](v)(x,t)

E*(D(II))(x)*(D[1](psi))(x, t)+E*II(x)*(D[1, 1](psi))(x, t)-G*A(x)*psi(x, t)+G*A(x)*(D[1](v))(x, t)

 (1)
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convert(eq1,diff)

E*(diff(II(x), x))*(diff(psi(x, t), x))+E*II(x)*(diff(diff(psi(x, t), x), x))-G*A(x)*psi(x, t)+G*A(x)*(diff(v(x, t), x))

 (2)
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eq2:=-(G*D[1](A)(x)*psi(x,t)+G*A(x)*D[1](psi)(x,t))+(G*D[1](A)(x)*v(x,t))+G*A(x)*(D[1]@@2)(v)(x,t)-m(x)/G*D[2](v)(x,t)

-G*(D(A))(x)*psi(x, t)-G*A(x)*(D[1](psi))(x, t)+G*(D(A))(x)*v(x, t)+G*A(x)*(D[1, 1](v))(x, t)-m(x)*(D[2](v))(x, t)/G

 (3)
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convert(%,diff)

-G*(diff(A(x), x))*psi(x, t)-G*A(x)*(diff(psi(x, t), x))+G*(diff(A(x), x))*v(x, t)+G*A(x)*(diff(diff(v(x, t), x), x))-m(x)*(diff(v(x, t), t))/G

 (4)
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isolate(convert(eq2,diff),psi)

psi = (proc (x, t) options operator, arrow; -(G^2*A(x)*(diff(psi(x, t), x))-G^2*(diff(A(x), x))*v(x, t)-G^2*A(x)*(diff(diff(v(x, t), x), x))+m(x)*(diff(v(x, t), t)))/(G^2*(diff(A(x), x))) end proc)

 (5)
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eval(eq1,psi(x,t)=rhs((isolate(eq2,psi))(x,t))):convert(%,diff)

E*(diff(II(x), x))*(diff(psi(x, t), x))+E*II(x)*(diff(diff(psi(x, t), x), x))+A(x)*(G^2*A(x)*(diff(_XX(x, t), x))-G^2*A(x)*(diff(diff(v(x, t), x), x))-G^2*(diff(A(x), x))*v(x, t)+m(x)*(diff(v(x, t), t)))/(G*(diff(A(x), x)))+G*A(x)*(diff(v(x, t), x))

 (6)
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