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How to specify - Differential equation initial conditions

Posted 9 years ago

I have inputted the following differential equation into Wolfram Alpha:

d^2y/dx^2+3dy/dx+2y=e^t

I am struggling to work out how specify that y=1 and dy/dx=0 at t=0, so that I can find the particular solution.

Any help would be greatly appreciated!

POSTED BY: Jason Craigs
2 Replies

The conditions are evidently incomplete:

In[8]:= DSolve[{D[y[x, t], {x, 2}] + 3 D[y[x, t], x] + 2 y[x, t] == 
   E^t, y[x, 0] == 1, D[y[x, 0], x] == 0}, y[x, t], {x, t}]

During evaluation of In[8]:= DSolve::bvnr: For some branches of the general solution, the given boundary conditions do not restrict the existing freedom in the general solution. >>

During evaluation of In[8]:= DSolve::bvsing: Unable to resolve some of the arbitrary constants in the general solution using the given boundary conditions. It is possible that some of the conditions have been specified at a singular point for the equation. >>

Out[8]= {{y[x, t] -> 
   1/2 E^(-2 x) (E^(t + 2 x) + 2 C[1][t] + 2 E^x C[2][t])}}
POSTED BY: S M Blinder
Posted 9 years ago
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