1)First and most important, do not give Yi(t) history as feature. You will just end in a model that replicates the previous input to minimize the error, a cheating model. For more detail, you can have a look at my explanations at two different questions:
2)Create your labels by sliding your Y(t) one step forward so that your each sample will have a label of Y(t+1). That means you will delete sample #1 as a result.
3)Use a time-window for each sample for your features. Do not provide just your features as x(t) for the label y(t+1). For example, with a window size w = 10, provide x(t-9),x(t-8),.....,x(t-1),x(t+1) as a single sample for label y(t+1). Then you will be boosting the sequential nature of LSTM, possibly acquiring greater performance.
4)You can use Keras for your LSTM regression task, have a look at simple code piece from my old works, I modified it for your task:
nn = Sequential()
nn.add(LSTM(80, batch_input_shape=(64,11,20), return_sequences=True, recurrent_dropout = 0.1))
nn.add(LSTM(60, recurrent_dropout = 0.2))
nn.compile(loss= 'mse, optimizer= 'adam')
nn.fit(x_train, y_train, epochs=15, batch_size=64, shuffle=True, validation_data=(x_dev, y_dev))
y_pred = nn.predict(x_dev, batch_size=64)
where batch_input_shape=(64,10,25) explains that your batch size is 64 (trains 64 samples per gradient descent), your window size is 10, and you have 25 different features. You can delete anything about dropout in the code if you get confused; they are just for preventing overfitting.
Note: Do not forget to normalize your numeric input data at the start!
Hope I could help. Good Luck!