Psalm 55:22: "Cast your burden on the LORD, and he will sustain you; he will never permit the righteous to be moved."
Proverbs 3:5-6: "5 Trust in the LORD with all your heart, and do not lean on your own understanding. 6 In all your ways acknowledge him, and he will make straight your paths."
Isaiah 41:10: "fear not, for I am with you; be not dismayed, for I am your God; I will strengthen you, I will help you, I will uphold you with my righteous right hand."
Matthew 9:22: "Jesus turned, and seeing her he said, 'Take heart, daughter; your faith has made you well.' And instantly the woman was made well."
+++
The text is public domain:
1 If thou but trust in God to guide theeAnd hope in Him through all thy ways,He'll give thee strength, whate'er betide thee,And bear thee through the evil days.Who trusts in God's unchanging loveBuilds on the rock that naught can move.2 What can these anxious cares avail thee,These never-ceasing moans and sighs?What can it help if thou bewail theeO'er each dark moment as it flies?Our cross and trials do but pressThe heavier for our bitterness.3 Be patient and await His leisureIn cheerful hope, with heart contentTo take whate'er thy Father's pleasureAnd His discerning love hath sent,Nor doubt our inmost wants are knownTo Him who chose us for His own.4 God knows full well when times of gladnessShall be the needful thing for thee.When He has tried thy soul with sadnessAnd from all guile has found thee free,He comes to thee all unawareAnd makes thee own His loving care.5 Nor think amid the fiery trialThat God hath cast thee off unheard,That he whose hopes meet no denialMust surely be of God preferred.Time passes and much change doth bringAnd sets a bound to ev'rything.6 All are alike before the Highest;'Tis easy for our God, we know,To raise thee up, though low thou liest,To make the rich man poor and low.True wonders still by Him are wroughtWho setteth up and brings to naught.7 Sing, pray, and keep His ways unswerving,Perform thy duties faithfully,And trust His Word; though undeserving,Thou yet shalt find it true for thee.God never yet forsook in needThe soul that trusted Him indeed.
+++
Psalm 55:22 and Isaiah 41:10 appear in the lines "He'll give thee strength, whate'er betide thee, / And bear thee through the evil days" in the first verse. Psalm 55:22 (specifically "he will never permit the righteous to be moved") could also be cited for the lines "Who trusts in God's unchanging love / Builds on the rock that naught can move," although the imagery there seems to be taken from Matthew 7:24-25.
Proverbs 3:5-6 appears in the first verse, in the lines "If thou but trust in God to guide thee / And hope in Him through all thy ways," and it's also the foundation for the entire hymn.
Matthew 9:22 seems to be the basis for the seventh verse.
+++
The line "What can these anxious cares avail thee" at the beginning of the second verse is similar to Jesus' rhetorical question "'And which of you by being anxious can add a single hour to his span of life?'" in Matthew 6:27 and Luke 12:25.