Quick questions on Differential equations - TCE Mathematics Specialised (Tasmania)

Q: What are separable equations?

An equation is separable if it can be written dydx = f(x)g(y). Rearrange so each variable is with its own differential, then integrate both sides: $int (1)/(g(y))\, dy = int f(x)\, dx.$

Q: What are first order linear equations?

A first order linear equation has the standard form $(dy)/(dx) + P(x)\, y = Q(x).$

2short Q&A pairs drawn directly from our worked dot-point answer. For full context and worked exam questions, read the parent dot-point page.

What are separable equations?

Show answer

An equation is separable if it can be written

\tfrac{dy}{dx} = f(x)g(y)

. Rearrange so each variable is with its own differential, then integrate both sides: $

\int \frac{1}{g(y)}\, dy = \int f(x)\, dx.

What are first order linear equations?

Show answer

A first order linear equation has the standard form $

\frac{dy}{dx} + P(x)\, y = Q(x).

Have a question we have not covered?

This dot-point answer is short enough that we have not extracted many short questions yet. Read the full dot-point answer or ask Mo, our study assistant, in the chat for follow ups.

All Specialist MathematicsQ&A pages