Order and solutions to differential equations - Differential Equations

Intro Lesson

• a)

  Notation and Order of a Differential Equation

• b)

  Solution to a Differential Equation

• c)

  Particular Solutions

• a)

  $y''' = {t^2} + 7$

• b)

  $y''( t ) + 6y'( t ) + 8y( t ) = ln( t )$

• c)

  $5\frac{{dy}}{{dt}} = \csc \left( {4t} \right) + \frac{{{d^2}y}}{{d{t^2}}}$

• d)

  ${x^3}\frac{{{d^3}y}}{{d{x^3}}} + {x^2}\frac{{{d^2}y}}{{d{x^2}}} + x\frac{{dy}}{{dx}} = 1$

• a)

  $y = \cos( 5t )$ is a solution to $y'' + 25y =$0

• b)

  $y = C\cos \left( {5t} \right)$ is a solution to $y'' + 25y =$0 where $C$ is a constant

• c)

  $y = C{e^x}$ is a solution to $3y + y' + y'' - 3y''' = 2C{e^x}$ where $C$ is a constant

• d)

  $y = \frac{{{x^4}}}{4} + {x^2}$ is a solution to $y''' = 6x$

• a)

  $6{x^3} + 9{y^2} = C$ where $y\left( 0 \right) = 3$

• b)

  $C{e^{3t}} = {y^2}$ where $y\left( 1 \right) = 1$