AJSesinando
Identifying Linear First-Order Equations and the Superposition Principle in Differential Equations
A linear first-order differential equation is one you can write as y-dot plus p(x) times y equals q(x), and you check this form to know whether you can use linear methods on it. The superposition principle says that if y1 and y2 are solutions for two right-hand sides, then y1 plus y2 is a solution for the sum of those right-hand sides. Every linear equation obeys superposition, and a non-linear equation such as y-dot plus y squared equals q(t) breaks it. This lets you test an equation and explains why linear equations are studied so much.