Solving Differential Equations

0 of 0 exercises completed

An introduction to differential equations and how to solve them.

Want a deeper conceptual understanding? Try our interactive lesson!

Separable Variables

AHL 5.18

When you have a differential equation in the form

dxdy=f(x)g(y)🚫

you can bring all the y's to one side and all the x's to the other:

g(y)1dy=f(x)dx🚫

∫g(y)1dy=∫f(x)dx🚫

Particular Solutions

AHL 5.18

The solutions to differential equations will usually contain a constant of integration +C. These are called general solutions.

Often, we are given an initial condition, ie the value of y for a specific x, which we can use to solve for C. The result is the particular solution.

Direct Integration

AHL 5.18

The easiest differential equations to solve are the ones in the form

dxdy=f(x)

as we can simply integrate:

y=∫f(x)dx🚫

Integrating Factor

AHL 5.18

For a differential equation in the form

dxdy+P(x)y=Q(x)

Multiply both sides by integrating factor (often called μ):

e∫P(x)dx📖

and notice the product rule on the LHS.

Homogeneous Equation

AHL 5.18

dxdy=f(xy)🚫

Let y=vx, then v=xy.

Note: On IB exams you will be told to use the substitution y=vx.

Nice work completing Solving Differential Equations, here's a quick recap of what we covered:

Skills covered

Mixed Practice

Exercises checked off

I'm Plex, here to help you understand this concept!

Euler's Method

Differential Equations

Solving Differential Equations

0 of 0 exercises completed

An introduction to differential equations and how to solve them.

Want a deeper conceptual understanding? Try our interactive lesson!

Separable Variables

AHL 5.18

When you have a differential equation in the form

dxdy=f(x)g(y)🚫

you can bring all the y's to one side and all the x's to the other:

g(y)1dy=f(x)dx🚫

∫g(y)1dy=∫f(x)dx🚫

Particular Solutions

AHL 5.18

The solutions to differential equations will usually contain a constant of integration +C. These are called general solutions.

Often, we are given an initial condition, ie the value of y for a specific x, which we can use to solve for C. The result is the particular solution.

Direct Integration

AHL 5.18

The easiest differential equations to solve are the ones in the form

dxdy=f(x)

as we can simply integrate:

y=∫f(x)dx🚫

Integrating Factor

AHL 5.18

For a differential equation in the form

dxdy+P(x)y=Q(x)

Multiply both sides by integrating factor (often called μ):

e∫P(x)dx📖

and notice the product rule on the LHS.

Homogeneous Equation

AHL 5.18

dxdy=f(xy)🚫

Let y=vx, then v=xy.

Note: On IB exams you will be told to use the substitution y=vx.

Nice work completing Solving Differential Equations, here's a quick recap of what we covered:

Skills covered

Mixed Practice

Exercises checked off

I'm Plex, here to help you understand this concept!

Euler's Method

Differential Equations

Solving Differential Equations

0 of 0 exercises completed

An introduction to differential equations and how to solve them.

Want a deeper conceptual understanding? Try our interactive lesson!

Separable Variables

AHL 5.18

When you have a differential equation in the form

dxdy=f(x)g(y)🚫

you can bring all the y's to one side and all the x's to the other:

g(y)1dy=f(x)dx🚫

∫g(y)1dy=∫f(x)dx🚫

Particular Solutions

AHL 5.18

The solutions to differential equations will usually contain a constant of integration +C. These are called general solutions.

Often, we are given an initial condition, ie the value of y for a specific x, which we can use to solve for C. The result is the particular solution.

Direct Integration

AHL 5.18

The easiest differential equations to solve are the ones in the form

dxdy=f(x)

as we can simply integrate:

y=∫f(x)dx🚫

Integrating Factor

AHL 5.18

For a differential equation in the form

dxdy+P(x)y=Q(x)

Multiply both sides by integrating factor (often called μ):

e∫P(x)dx📖

and notice the product rule on the LHS.

Homogeneous Equation

AHL 5.18

dxdy=f(xy)🚫

Let y=vx, then v=xy.

Note: On IB exams you will be told to use the substitution y=vx.

Nice work completing Solving Differential Equations, here's a quick recap of what we covered:

Skills covered

Mixed Practice

Exercises checked off

I'm Plex, here to help you understand this concept!

Generating starter questions...

Euler's Method

Differential Equations

Solving Differential Equations

0 of 0 exercises completed

An introduction to differential equations and how to solve them.

Want a deeper conceptual understanding? Try our interactive lesson!

Separable Variables

AHL 5.18

When you have a differential equation in the form

dxdy=f(x)g(y)🚫

you can bring all the y's to one side and all the x's to the other:

g(y)1dy=f(x)dx🚫

∫g(y)1dy=∫f(x)dx🚫

Particular Solutions

AHL 5.18

The solutions to differential equations will usually contain a constant of integration +C. These are called general solutions.

Often, we are given an initial condition, ie the value of y for a specific x, which we can use to solve for C. The result is the particular solution.

Direct Integration

AHL 5.18

The easiest differential equations to solve are the ones in the form

dxdy=f(x)

as we can simply integrate:

y=∫f(x)dx🚫

Integrating Factor

AHL 5.18

For a differential equation in the form

dxdy+P(x)y=Q(x)

Multiply both sides by integrating factor (often called μ):

e∫P(x)dx📖

and notice the product rule on the LHS.

Homogeneous Equation

AHL 5.18

dxdy=f(xy)🚫

Let y=vx, then v=xy.

Note: On IB exams you will be told to use the substitution y=vx.

Nice work completing Solving Differential Equations, here's a quick recap of what we covered:

Skills covered

Mixed Practice

Exercises checked off

I'm Plex, here to help you understand this concept!

Generating starter questions...