Following are a set of lectures by much-revered professor Gilbert Strang on differential equations.

https://ocw.mit.edu/resources/res-18-009-learn-differential-equations-up-close-with-gilbert-strang-and-cleve-moler-fall-2015/differential-equations-and-linear-algebra/introduction/overview-of-differential-equations

https://ocw.mit.edu/resources/res-18-009-learn-differential-equations-up-close-with-gilbert-strang-and-cleve-moler-fall-2015/differential-equations-and-linear-algebra/introduction/the-calculus-you-need

By the way, I was wondering that why do we multiply with the exponent while taking derivatives (if you remember the power rule). I looked up on the Internet and found this cool explanation on Coursera.

https://www.coursera.org/learn/calculus1/lecture/WifyU/how-do-we-justify-the-power-rule

https://ocw.mit.edu/resources/res-18-009-learn-differential-equations-up-close-with-gilbert-strang-and-cleve-moler-fall-2015/differential-equations-and-linear-algebra/first-order-equations/response-to-exponential-input

https://ocw.mit.edu/resources/res-18-009-learn-differential-equations-up-close-with-gilbert-strang-and-cleve-moler-fall-2015/differential-equations-and-linear-algebra/first-order-equations/solution-for-any-input

https://ocw.mit.edu/resources/res-18-009-learn-differential-equations-up-close-with-gilbert-strang-and-cleve-moler-fall-2015/differential-equations-and-linear-algebra/first-order-equations/step-function-and-delta-function

https://ocw.mit.edu/resources/res-18-009-learn-differential-equations-up-close-with-gilbert-strang-and-cleve-moler-fall-2015/differential-equations-and-linear-algebra/first-order-equations/response-to-complex-exponential

https://ocw.mit.edu/resources/res-18-009-learn-differential-equations-up-close-with-gilbert-strang-and-cleve-moler-fall-2015/differential-equations-and-linear-algebra/first-order-equations/integrating-factor-for-constant-rate

https://ocw.mit.edu/resources/res-18-009-learn-differential-equations-up-close-with-gilbert-strang-and-cleve-moler-fall-2015/differential-equations-and-linear-algebra/first-order-equations/integrating-factor-for-a-varying-rate

https://ocw.mit.edu/resources/res-18-009-learn-differential-equations-up-close-with-gilbert-strang-and-cleve-moler-fall-2015/differential-equations-and-linear-algebra/first-order-equations/the-logistic-equation

The Stability and Instability of Steady States

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https://ocw.mit.edu/resources/res-18-009-learn-differential-equations-up-close-with-gilbert-strang-and-cleve-moler-fall-2015/differential-equations-and-linear-algebra/first-order-equations/separable-equations

Second Order Equations

Description: For the oscillation equation with no damping and no forcing, all solutions share the same natural frequency. Related section in textbook: 2.1 Instructor: Prof. Gilbert Strang

Forced Harmonic Motion

Description: When the forcing is a sinusoidal input, like a cosine, one particular solution has the same form. But if the forcing frequency equals the natural frequency there is resonance. Related section in textbook: 2.1b Instructor: Prof. Gilbert Strang

Unforced Damped Motion

Description: With constant coefficients in a differential equation, the basic solutions are exponentials. The exponent solves a simple equation. Related section in textbook: 2.3 Instructor: Prof. Gilbert Strang

Photo by Jonas B