Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.

Please verify your account before proceeding.

In this lesson, we will learn how to solve first-order differential equations.

Q1:

Consider the differential equation π¦ β² + π¦ = 0 . Suppose that a student determined the solution to be π¦ = π π₯ . Based upon this information, is the student correct?

Q2:

Find the general solution for the following higher-order differential equation: π¦ β² β² β² + 9 π¦ β² β² + 2 7 π¦ β² + 2 7 π¦ = 0 .

Q3:

The one-dimensional time-independent Schrodinger equation is given as

where π is a wave function which describes the displacement π₯ of a single particle of mass π , πΈ is the total energy, π is the potential energy, and β is a known constant. Since π ( π₯ ) = 0 for the particle-in-a-box model, where 0 β€ π₯ β€ π , this second-order differential equation becomes

Find the general solution for this differential equation.

Q4:

Find the general solution for the following homogeneous ordinary differential equation with constant coefficients: π¦ β 2 π¦ + π¦ = 0 ο ο ο .

Donβt have an account? Sign Up