"Though I was very young, the plan of salvation was so clear to my mind, and my personal experience had been so marked, that, upon considering the matter, I knew it was my duty to continue my efforts for the salvation of precious souls, and to pray and confess Christ at every opportunity. My entire being was offered to the service of my Master. Let come what would, I determined to please God, and live as one who expected the Saviour to come and reward the faithful. I felt like a little child coming to God as to my father, and asking Him what He would have me to do. Then as my duty was made plain to me, it was my greatest happiness to perform it. Peculiar trials sometimes beset me. Those older in experience than myself endeavored to hold me back and cool the ardor of my faith; but with the smiles of Jesus brightening my life, and the love of God in my heart, I went on my way with a joyful spirit. LS 42.2"
Both passages express a desire to be taught and guided by God. EGW describes feeling like a child asking God what He would have her do, while Psalm 86:11 directly asks God to teach His way. Both express a commitment to following God's will.
"In losing sight of the true character of Jehovah, the Israelites were without excuse. Often had God revealed Himself to them as one “full of compassion, and gracious, long-suffering, and plenteous in mercy and truth.” Psalm 86:15 . “When Israel was a child,” He testified, “then I loved him, and called My son out of Egypt.” Hosea 11:1 . PK 311.2"
Ellen White directly references Psalms 86:15 in this passage.