2.1.44 \(3 u_x+2 u_y=0\) with \(u(x,0)=\sin x\). Problem 3.5(a) Lokenath Debnath

problem number 44

Added June 3, 2019.

Problem 3.5(a) nonlinear pde’s by Lokenath Debnath, 3rd edition.

Solve for \(u(x,y)\)

\[ 3 u_x+2 u_y=0 \]

with \(u(x,0)=\sin x\)

Mathematica ✓

ClearAll["Global`*"]; 
pde =  3*D[u[x, y], x] + 2*D[u[x,y],y] == 0; 
ic  = u[x,0]==Sin[x]; 
sol =  AbsoluteTiming[TimeConstrained[DSolve[{pde,ic} ,u[x, y], {x, y}], 60*10]];
 

\[\left \{\left \{u(x,y)\to \sin \left (x-\frac {3 y}{2}\right )\right \}\right \}\]

Maple ✓

restart; 
pde :=3*diff(u(x,y),x)+ 2*diff(u(x,y),y)= 0; 
ic  := u(x,0)=sin(x); 
cpu_time := timelimit(60*10,CodeTools[Usage](assign('sol',pdsolve([pde,ic],u(x,y))),output='realtime'));
 

\[u \left (x , y\right ) = \sin \left (x -\frac {3 y}{2}\right )\]

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