7.1.4 1.4

7.1.4.1 [2012] Problem 1

problem number 2012

Added March 23, 2019.

Problem Chapter 1.1.4.1, from Handbook of nonlinear partial differential equations by Andrei D. Polyanin, Valentin F. Zaitsev.

Solve for \(w(x,t)\)

\[ w_t = a w_{xx} +s_1 (b x+c t)^k+ s_2 w^m \]

Mathematica ✗

ClearAll["Global`*"]; 
pde = D[w[x, t], t] == a*D[w[x, t], {x, 2}] + s1*(b*x + c*t)^k + s2*w[x, t]^m; 
sol =  AbsoluteTiming[TimeConstrained[DSolve[pde, w[x, t], {x, t}], 60*10]];
 

Failed

Maple ✗

restart; 
pde :=  diff(w(x,t),t)= a*diff(w(x,t),x$2) +s1*(b*x+c*t)^k+s2*w(x,t)^m; 
cpu_time := timelimit(60*10,CodeTools[Usage](assign('sol',pdsolve(pde,w(x,t))),output='realtime'));
 

sol=()