I'm solving a differential equation in Mathematica. Here is what I'm solving:
DSolve[{-(r V[w])+u V'[w]+s V''[w]==-E^(g w)},V[w],w]
When I use Wolfram Alpha to solve it, it gives me a nice solution:
solve u*V'(w) + s*V''(w) - r * V = -exp(g*w)
V(w) = c_1 e^((w (-sqrt(4 r s+u^2)-u))/(2 s))+c_2 e^((w (sqrt(4 r s+u^2)-u))/(2 s))+e^(g w)/(r-g (g s+u))
But when I use Mathematica, the solution is long and ugly:
{{V[w] -> (2 s (2 E^(((2 g s + u - Sqrt[4 r s + u^2]) w)/( 2 s) + ((-u + Sqrt[4 r s + u^2]) w)/(2 s)) g s - 2 E^(((-u - Sqrt[4 r s + u^2]) w)/( 2 s) + ((2 g s + u + Sqrt[4 r s + u^2]) w)/(2 s)) g s + E^(((2 g s + u - Sqrt[4 r s + u^2]) w)/( 2 s) + ((-u + Sqrt[4 r s + u^2]) w)/(2 s)) u - E^(((-u - Sqrt[4 r s + u^2]) w)/( 2 s) + ((2 g s + u + Sqrt[4 r s + u^2]) w)/(2 s)) u + E^(((2 g s + u - Sqrt[4 r s + u^2]) w)/( 2 s) + ((-u + Sqrt[4 r s + u^2]) w)/(2 s)) Sqrt[ 4 r s + u^2] + E^(((-u - Sqrt[4 r s + u^2]) w)/( 2 s) + ((2 g s + u + Sqrt[4 r s + u^2]) w)/(2 s)) Sqrt[ 4 r s + u^2]))/(Sqrt[ 4 r s + u^2] (-2 g s - u + Sqrt[4 r s + u^2]) (2 g s + u + Sqrt[4 r s + u^2])) + E^(((-u - Sqrt[4 r s + u^2]) w)/(2 s)) C[1] + E^(((-u + Sqrt[4 r s + u^2]) w)/(2 s)) C[2]}}
Ew!
In general I would like Mathematica to give me a nice solution, the way Wolfram Alpha does. Does anyone know if I am missing and conditions? Or am I doing things wrong? Thanks!
