{{y[x] -> C[1] Cos[x] + Sin[x]}}
Simplify[
DSolve[ x (1-x^
2) y'[x] + (2x^
2-1) y[x]- x^
3 y^
3 == 0,
y[x], x] ]
3 2 {{y[x] -> x (y + Sqrt[1 - x ] C[1])}}Simplify[ DSolve[ y''[x] + 4y'[x] + 4y[x] - x Exp[x] == 0, y[x], x ] ]
x x -2 E E x C[1] x C[2] {{y[x] -> ----- + ---- + ---- + ------}} 27 9 2 x 2 x E E