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Ahmed111

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What kind of solution is it ?...

Ahmed111 130 Maple 2022
ode dsolve differential-equations
December 20 2022
1 0

What kind of solution is it (see (3))? Why is there no solution when I put the initial condition v(0)=C1? Secondly, eq. (2) can be reduced to a first-order differential equation?

> 

restart
> 

interface(showassumed = 0)

declare(v(y))

 (1)
> 

q := v(y)*(diff(diff(diff(v(y), y), y), y))+(2*v(y)-(diff(v(y), y)))*(diff(diff(v(y), y), y))+(diff(v(y), y))*(v(y)^3+v(y)-(diff(v(y), y))) = 0

v(y)*(diff(diff(diff(v(y), y), y), y))+(2*v(y)-(diff(v(y), y)))*(diff(diff(v(y), y), y))+(diff(v(y), y))*(v(y)^3+v(y)-(diff(v(y), y))) = 0

 (2)
> 

dsolve(q)

v(y) = ODESolStruc(_a, [{(diff(diff(_b(_a), _a), _a))*_b(_a)^2+_b(_a)*((diff(_b(_a), _a))^2*_a+_a^3-(diff(_b(_a), _a))*_b(_a)+2*(diff(_b(_a), _a))*_a-_b(_a)+_a)/_a = 0}, {_a = v(y), _b(_a) = diff(v(y), y)}, {y = Int(1/_b(_a), _a)+_C1, v(y) = _a}])

 (3)
> 

NULL
> 

dsolve({q, v(0) = C1})

v(y) = C1

 (4)
> 

NULL

Download CD_ode.mw

Error, (in Optimization:-NLPSolve)...

Ahmed111 130 Maple 2022
optimization
November 29 2022
3 3

I try to find the value of the highest peak by using Optimization. But Maple returns an error with the comment "Error, (in Optimization:-NLPSolve) abs is not differentiable at non-real arguments". How to remove it?

plot.mw

How can we draw the pot function?...

Ahmed111 130 Maple 2022
plotting incomplete-question
November 24 2022
1 2

How can we draw the pot function the same as in the attached figure (namely 'pot.png')? The values of V(x) may not be the same.

pot.mw

Error in dchange...

Ahmed111 130 Maple 2022
pde differential-equations dchange
November 16 2022
1 2

dchange gives the error when I try to convert pde into ode. Why?

> 

restarts
> 

with(PDEtools)
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pde1 := diff(u(x, t), t)-(diff(u(x, t), `$`(x, 2), t))+3*u(x, t)^2*(diff(u(x, t), x))-2*(diff(u(x, t), x))*(diff(u(x, t), `$`(x, 2)))-u(x, t)*(diff(u(x, t), `$`(x, 3))) = 0

diff(u(x, t), t)-(diff(diff(diff(u(x, t), t), x), x))+3*u(x, t)^2*(diff(u(x, t), x))-2*(diff(u(x, t), x))*(diff(diff(u(x, t), x), x))-u(x, t)*(diff(diff(diff(u(x, t), x), x), x)) = 0

 (1)
> 

trans1 := {seq(var[i] = tau[i], i = 2), FN = Y(zz), var[1] = (zz-(sum(lambda[i]*tau[i], i = 2)))/lambda[1]}

{FN = Y(zz), var[1] = (-lambda[2]*tau[2]+zz)/lambda[1], var[2] = tau[2]}

 (2)
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ode1 := dchange(trans1, pde, [Y(zz), zz, seq(tau[i], i = 2)])

Error, (in dchange/info) the number of new and old independent variables must be the same. Found {zz, tau[2]} as new, while {FN, var[1], var[2]} as old

  
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op(lhs(pde1))

diff(u(x, t), t), -(diff(diff(diff(u(x, t), t), x), x)), 3*u(x, t)^2*(diff(u(x, t), x)), -2*(diff(u(x, t), x))*(diff(diff(u(x, t), x), x)), -u(x, t)*(diff(diff(diff(u(x, t), x), x), x))

 (3)
> 

 

Download P_O.mw

How can we get the single possible solut...

Ahmed111 130 Maple 2020
ode dsolve differential-equations
October 06 2022
4 2

I solved the differential equation using 'dsolve' and Maple returns it with fiver possible solutions. How can we get the single possible solution for w(x) if we assume c, g (constants) are positive? Also, can we convert JacobiSN() to a simple trigonometric or algebraic function?

> 

restart
> 

with(DEtools)
> 

``
> 

q := (1/2)*(diff(w(x), x))^2+(1/8)*w(x)^4-(1/2)*c*w(x)^2-g = 0

(1/2)*(diff(w(x), x))^2+(1/8)*w(x)^4-(1/2)*c*w(x)^2-g = 0

 (1)
> 

dsolve((1/2)*(diff(w(x), x))^2+(1/8)*w(x)^4-(1/2)*c*w(x)^2-g = 0, {w(x)})

w(x) = (2*c+2*(c^2+2*g)^(1/2))^(1/2), w(x) = (-2*(c^2+2*g)^(1/2)+2*c)^(1/2), w(x) = -(2*c+2*(c^2+2*g)^(1/2))^(1/2), w(x) = -(-2*(c^2+2*g)^(1/2)+2*c)^(1/2), w(x) = 2*JacobiSN((1/2)*(-2*c+2*(c^2+2*g)^(1/2))^(1/2)*x+_C1, ((c*(c^2+2*g)^(1/2)-c^2-g)*g)^(1/2)/(c*(c^2+2*g)^(1/2)-c^2-g))*g/(g*(-c+(c^2+2*g)^(1/2)))^(1/2)

 (2)
> 

``

``

Download solve.mw

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