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On this page, you can find some differential equations handouts! People told me those handouts were really helpful while they were studying/doing their homework. Feel free to read those instead of the differential equations book!
Second-Order Differential Equations (Chapter 4)
Higher-Order Differential Equations (Chapter 6)
Systems of Differential Equations (Chapter 9)
Fourier Series and Partial Differential Equations (Chapter 10)