Yes, lysogenic viruses inject their DNA into the host cell, just like lytic viruses. However, there's a crucial difference in what happens after the injection.

Here's the breakdown:

* Lytic viruses: After injecting their DNA, they immediately take over the host cell's machinery to replicate themselves. This leads to the lysis (bursting) of the host cell and the release of new virus particles.

* Lysogenic viruses: After injecting their DNA, they integrate their genetic material into the host cell's genome. This integrated DNA is called a prophage. The prophage remains dormant, replicating along with the host cell's DNA.

The key difference:

* Lytic viruses immediately start replicating and destroy the host cell.

* Lysogenic viruses integrate their DNA into the host cell's genome and remain dormant, replicating passively along with the host cell.

It's important to note that lysogenic viruses can eventually switch to the lytic cycle under certain conditions, such as stress or environmental changes. This transition can lead to the production of new viruses and the destruction of the host cell.