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In the paper we describe the derivations of two $\mathbb{N}$-gradedinfinity-dimensional Lie algebras $\mathbf{n}_1$ and $\mathbf{n}_1$ what arepositive parts of affine Kats-Moody algebras $A^{(1)}_1$ and $A^{(2)}_2$,respectively. Then we construct all pro-solvable Lie algebras whose potentialnilpotent ideals are $\mathbf{n}_1$ and $\mathbf{n}_2$. For two specificrepresentatives of these classes low-dimensional (co)homology groups arecomputed.

On derivations and low-dimensional (co)homology groups of pro-sovable Lie algebras associated with $\mathbf{n}_1$ and $\mathbf{n}_2$