Solwant to solve a 2nd ving a partial differential equation with textbook solution - Printable Version +- HP Forums (https://www.hpmuseum.org/forum) +-- Forum: HP Calculators (and very old HP Computers) (/forum-3.html) +--- Forum: HP Prime (/forum-5.html) +--- Thread: Solwant to solve a 2nd ving a partial differential equation with textbook solution (/thread-20504.html) |
Solwant to solve a 2nd ving a partial differential equation with textbook solution - Anthony The Koala - 09-15-2023 08:56 AM First I managed to solve a 2nd order ode using the symbolic letters as in: desolve(∂(∂u/∂x)∂x+3*∂u/∂x=0,x,y) Now want to solve a 2nd order partial differential equation, pde My Reference for a textbook solution is from the book "Advanced Mathematics For Engineering Students", page 131. In the textbook The 2nd order pde is ∂2u/(∂x∂y) = 2x - y. The general solution is: u = x^2*y - 1/2*x*y^2 + F(x) + G(y) Where: F(x) = 2* sin(x) and G(y) = 3*y^4- 5 Entering the pde in the Prime [/b][/align]n CAS mode: b]desolve(∂(∂u/∂y)∂x+y-2*x=0,x,y,u)[/b] The answer is [1/2*y] It was not the textbook's answer. Question: why didn't the output from the prime match the textbook answer?[b] Thank you, Anthony, Sydney RE: partial differential equation with textbook solution - Albert Chan - 09-15-2023 12:18 PM (09-15-2023 08:56 AM)Anthony The Koala Wrote: In the textbook F(x) and G(y) can be any expression, that particular set is just for illustration. diff(u, y, x), both F(x) and G(y) goes away, leaving just (2x - y) From XCas manual, desolve(de, <x, y>), where x is variable, y is unknown. desolve may not be able to handle more variables. (it has other limits, see manual) We do this in steps (1 variable, 1 unknown). let w = diff(u,y) Cas> desolve(diff(w, x) = (2*x - y), x, w) -x*y + x^2 + G_0 Cas> desolve(diff(u, y) = (-x*y + x^2), y, u) Cas> expand(Ans) -1/2*x*y^2 + x^2*y + G_0 Or, we simplify integrate twice, to get u Cas> int(int((2*x - y), x), y) -1/2*x*y^2 + x^2*y u = x^2*y - 1/2*x*y^2 + F(x) + G(y), same as textbook answer RE: Solwant to solve a 2nd ving a partial differential equation with textbook solution - Anthony The Koala - 09-16-2023 01:56 AM Dear Mr Chan, Thank you for the reply. It is a learning experience of the limitations of the Prime not being able to handle PDEs. I tried your two-stage solution and it works. I wanted to go deeper by breaking down the statement desolve(diff(w, x) = (2*x - y), x, w) and do diff(w, x) = (2*x - y), x, w) The display said [diff(w,x)=2*x-y x w] [0=2*x-y x w] I tried b]diff(w, x) = (2*x - y))[/b] The display said [diff(w,x)=2*x-y] [0=2*x-y] I know desolve solves an ode but need further idea of what the Ans within the desolve does with [diff(w,x)=2*x-y x w] [0=2*x-y x w] ? [/b] Ref for the int command http://www.wiki4hp.com/doku.php?id=prime:programming:cas-calculus_commands Other question please Obviously there are many ways to solve a PDE including taking Laplace transforms and converting them to an ODE. Could the two-step method used in the original question be used to solve any kind of PDE and the need to specify the initial and boundary conditions? Thank you Anthony, Sydney[/i] |