Why do you think, your solution is wrong? It's perfectly right! It's the general solution of the equation (I've not checked it, but this you can do by taking the derivative and check whether it fulfills your equation), and whether you call the integration constant -C_3 or C doesn't matter.
The solution is made unique by giving, e.g., an initial value y(0)=y_0 as a constraint. If you use this in your and the textbook's answer you'll get the same result by choosing the right C_3 and C to match the initial-value constraint, respectively.