[Verse 1] When change depends on what you've got Y prime equals K times Y Population boom or nuclear rot Exponential curves that multiply Ce to the Kt, forever climbing Or crashing down with perfect timing [Chorus] Seven equations rule the world we see From growth to waves across the endless sea Y prime, Y double prime, and Del squared too These patterns govern all that physics knew Differential truths in motion Mathematical devotion [Verse 2] Y double prime plus omega squared Y Equals zero, springs will dance Cosine waves that never die Simple harmonic's perfect trance A cos of omega t plus phi Pendulums that kiss the sky [Chorus] Seven equations rule the world we see From growth to waves across the endless sea Y prime, Y double prime, and Del squared too These patterns govern all that physics knew Differential truths in motion Mathematical devotion [Verse 3] Add two gamma Y prime to the mix Damped oscillation takes the stage Friction's force that always tricks Swinging motion, turning page Energy bleeding, amplitude fading Real-world physics, not parading [Verse 4] Logistic growth knows limits well R times Y times one minus Y over K Sigmoid curves have tales to tell Carrying capacity holds sway Population growth constrained By resources that remained [Bridge] Del squared U equals zero flat Laplace speaks of equilibrium's art Heat equation with K Del squared that Makes temperatures slowly part Wave equation, c squared drives How disturbance propagates and thrives [Chorus] Seven equations rule the world we see From growth to waves across the endless sea Y prime, Y double prime, and Del squared too These patterns govern all that physics knew Differential truths in motion Mathematical devotion [Outro] From exponential's racing climb To waves that ripple space and time These seven hold the keys To nature's mysteries
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