Psalm 86 is a personal psalm of lament in which David expresses his grave concern about his lowly state and joys in the Lord who alone is merciful.  This is the only Psalm in Book III of the Psalms that has David’s title.  The whole Psalm can be divided into 6 sections:

1. A call for God to deliver David from distress (Ps 86:1-5)

2. A call for God to hear David’s prayer (Ps 86:6-7)

3. A statement that there is none other like God (Ps 86:8-10)

4. A petition for God to teach David deeper about God, that he can praise Him forever (Ps 86:11-13)

5. A comparison of the assault of the wicked with the character of the Lord (Ps 86:14-15)

6. A renewed call for God to show His goodness to David in his distress (Ps 86:16-17)

Jesus speaks of an undivided heart in the Sermon on the Mount: “Blessed are the pure in heart, for they shall see God." (Matthew 5:8)  The Greek word for pure is ‘katharos’ which describes a heart that is pure in motive exhibiting single-mindedness, undivided devotion and spiritual integrity. The word “Pure” (katharos) has to do with attitude, integrity and singleness of heart whereas our heart and mind are always distracted with various agonies and concerns of our day-to-day life and of the future. To be more precise, an undivided heart is a single-minded heart, dedicated to God, having one driving purpose—to live pleasing to God. Such a heart’s attention is fixed on God alone and does not allow itself to be distracted or influenced by the passing desires of sin or anything else. 

MacArthur adds (commenting on Matthew 5:8 "pure in heart") that in secular Greek usage, ‘katharos’ was often used of metals that had been refined until all impurities were removed, leaving only the metal. In that sense, purity means unmixed, unalloyed, unadulterated. Applied to the heart, the idea is that of pure motive of single-mindedness, undivided devotion, spiritual integrity, and true righteousness. 

The last part of Ps 86:11 is a combination of supplication and commitment: "Give me an undivided heart to revere your name." The implied meaning of these elements is that we need sound teaching so that we concentrate to walk in God's way. As the psalmist moves on, he does not dwell on the need for an undivided heart, for in the very next line he expresses: “I will praise you, O Lord my God, ‘with all my heart" (Ps 86:12). The Psalmist already won confidence in that moment that his prayer for an undivided heart is answered. For then there is a bold claim he makes in Ps 86:12: "I will glorify your name forever." Not only has he moved from revering to glorifying, but the addition of "forever" makes the return of thanks to God, all the more passionate. It is a strong statement of commitment as one can imagine! Can we make this claim as our own? 

The Psalmist closes the psalm with a final plea, a request for a sign of God's favor. We all sometimes pray to God for a sign as God’s guidance and it is right to pray for a sign from God in the light of Ps 86:17.  Hence we can take this as a model for our own prayer to God in certain situations based on our confidence in God's steadfast love and faithfulness to us in the past.

A Prayer to the Rock of Ages:

“From the end of the earth I will cry to You,

When my heart is overwhelmed;

Lead me to the rock that is higher than I.”

Psalm 61:2 (NKJV)

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Listen- 'Teach Me Your Way O Lord'