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# Category Archives: Differential Equations

## Differential Equations problems (complete Playlist)

Explore a variety of examples and practiceĀ problems in the Differential Equations course in the video playlist below.

## Calculus problems (complete Playlist)

Find a variety of Calculus examples and practiceĀ problems to help you improve in Calculus 1, Calculus 2, Calculus 3, and more courses.

Topics include limits, continuity, differentiation, integration, parametric equations, polar coordinates, sequences and series, application problems, and more!

## Complex Roots of the Characteristic Equation example question

In each of the given examples, use Euler’s formula to write the given expression in the form a + ib.

Solution to this Differential Equations practiceĀ problem is given in the video below!

## Wronskian of Functions example question

Find the Wronskian of the given pair of functions:

Solution to this Differential Equations practiceĀ problemĀ is given in the video below!

## Differential Equation with Constant Coefficients example question

Find the general solution of the given differential equation

Solution to this Differential Equations practiceĀ problemĀ is given in the video below!

## EXACT Differential Equation example question

Solve the differential equation

by first showing that it isĀ exact and then find the solution.

Solution to this Differential Equations practiceĀ problemĀ is given in the video below!

## First Order Differential Equation Modeling Tank example question

Consider a tank used in certain hydrodynamic experiments. After one experiment the tank contains 200 liters of a dye solution with a concentration of 1 gram per liter. To prepare for the next experiment, the tank is to be rinsed with fresh water flowing in at a rate of 2 liter per minute, the well-stirred solution flowing out at the same rate. Find the time that will elapse before the concentration of dye in the tank reaches 1% of its original value.

Solution to this Differential Equations practiceĀ problemĀ is given in the video below!

## Homogeneous Differential Equation Equation example question

Solve the differential equation

by showing it is homogeneous and separable and thenĀ find the solution.

Solution to this Differential Equations practiceĀ problemĀ is given in the video below!

## Separable Differential Equations example question

Solve the differential equation

by showing it is separable and then use Integration to find the solution.

Solution to this Differential Equations practiceĀ problemĀ is given in the video below!

## Differential Equation Integrating Factor example question

Solve the differential equation

by using the Integrating Factor solution method.

Solution to this Differential Equations practiceĀ problemĀ is given in the video below!