Class prep · TJ Differential Equations

Model the change,then explain the solution.

A first course in differential equations, from first-order models through linear equations and oscillations, Laplace transforms, systems, numerical methods and boundary-value problems. Connect equations, solution curves and the assumptions behind each model. Every problem has a full worked solution. Built by Neil Kothari, a TJ alumnus.

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$395 covers the full school year. The first lesson is free.

Try one. This is a test-level question from the course.

Problem 1

Test level
Multiple choice
No calculator
4 pts

For $y'=\sqrt{1+t^2+y^2}$ and $y(0)=0$ , what follows directly from the local theorem requiring continuity of $f$ and $\partial f/\partial y$ near the initial point?

original problems, each with a worked answer: 468; original problems, each with a worked answer
at test level or beyond: 324; at test level or beyond
short lessons, one for every topic: 36; short lessons, one for every topic
units, all open now: 6; units, all open now

Free lesson

Lesson 1.1: Models, Solutions and Direction Fields

Connect a differential equation to its solutions, local guarantees and valid intervals.

Start with a differential equation, check a proposed solution and connect it to a direction field.

Problem 2

Core
True or false
No calculator
2 pts

True or false: $y y'+t y=1$ is linear in $y$ because its highest derivative is first order.

Problem 3

Core
Multiple choice
No calculator
4 pts

The curve $t^2+y^2=10$ is to solve $y'=-t/y$ with $y(1)=3$ . Which formula and maximal open interval containing $1$ are correct?

Open the rest of this lesson, free

The full lesson and all 13 of its problems, with every worked answer.

How it works

Class prep that works alongside class

A complete Differential Equations course for students in grades 9 to 12. Work alongside your school course or study the material in sequence after calculus and basic linear algebra. Each lesson starts with a concrete example, develops the idea, and shows how to check your reasoning before you try the practice.

Original problems in several formats: true or false, multiple choice, multi-part and free response.
Each one is marked core, test level or beyond.
Choose a solution method, check initial conditions and domains, and connect exact calculations to qualitative behavior.
A worked answer for every problem, ending with the mistake that most often costs points.
A lesson on every topic, with diagrams wherever a geometric picture makes the idea clear.

What is inside

1First-Order Equations and Models6 lessons · 78 problems
2Linear Equations and Oscillations6 lessons · 78 problems
3Laplace Transform Methods6 lessons · 78 problems
4Linear Systems6 lessons · 78 problems
5Nonlinear Dynamics and Numerical Methods6 lessons · 78 problems
6Series and Boundary Value Problems6 lessons · 78 problems

The front entrance of Thomas Jefferson High School for Science and Technology

Who built it

Neil Kothari

TJHSST alumnus · Co-founder, EduAvenues · 10+ years in TJ preparation

Neil is a TJ alumnus and has spent more than a decade working with TJ students and their families. He built this course so students can connect exact solutions, qualitative behavior and the assumptions in a model. Every problem is written for the course and every answer is checked before it goes in.

Tuition

$395for the full school year

One tuition covers every unit of the course. All 6 units are open now. The Models, Solutions and Direction Fields lesson stays free for everyone.

All 6 units: 36 lessons and 468 original problems
A worked answer for every problem
Access through the end of the school year

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