Showing Superposition Principle with Time-Dependent Schrödinger Equation

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Homework Statement

Show that, if psi1 and psi2 are both solutions of the time-dependent Schr¨odinger
equation, so is c(subscipt1) psi1 + c(subscript2) psi2 (where c1 and c2 are arbitrary constants).

Homework Equations

The Attempt at a Solution

every source I've consulted so far just states it as a fact. i know its somthing to do with the superposition principle but how do i literally show what they ask? its only a 2 markk que
thanks in advance

 

[vela]

Just plug that combination into the Schrödinger equation and show it satisfies the equation.