There is no symphony by Beethoven and Mozart.

Beethoven's symphonies were:

• Symphony No. 1 in C major, op. 21 (1799-1800)
• Symphony No. 2 in D major, op.36 (1802)
• Symphony No. 3 in E flat major, op.55, "Eroica", (1804)
• Symphony No. 4 in B flat major, op. 60, (1806)
• Symphony No. 5 in C minor, op. 67 (1807)
• Symphony No. 6 in F major, op. 68,"Pastoral" (1808)
• Symphony No. 7 in A major, op. 92, "The Apotheosis of Dance", (1812)
• Symphony No. 8 in F major, op.93 "The Little Symphony"(1812)
• Symphony No. 9 with a choir and soloists, in D minor, op.125 (1817-1825) - the 'Choral'.

Yes. Beethoven wrote nine symphonies. They were:

• Symphony No. 1 in C major, op. 21 (1799-1800)
• Symphony No. 2 in D major, op.36 (1802)
• Symphony No. 3 in E flat major, op.55, "Eroica", (1804)
• Symphony No. 4 in B flat major, op. 60, (1806)
• Symphony No. 5 in C minor, op. 67 (1807)
• Symphony No. 6 in F major, op. 68,"Pastoral" (1808)
• Symphony No. 7 in A major, op. 92, "The Apotheosis of Dance", (1812)
• Symphony No. 8 in F major, op.93 "The Little Symphony"(1812)
• Symphony No. 9 with a choir and soloists, in D minor, op.125 (1817-1825) - the 'Choral'.

None of Beethoven's songs were symphonies. A song is a song; it involves an arrangement for voice with accompaniment. A symphony is an orchestral work.

Beethoven wrote over 160 songs, known as lieder, but only 9 symphonies.