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# ODE flash cards

### What method do you use to solve each ODE

Question | Answer |
---|---|

What method do you use for this equation y'(x)+a(x)y=b(x) ? | Using separation of variables where q(x)=exp^(∫a(x)dx) |

What method do you use for this equation g(y) y'(x)=b(x) ? | Integrate on both sides ∫g(y)dy=∫b(x)dx |

What method do you use for this equation y'(x)+a(x)y=b(x) y^n ? | This is a Bernoulli equation and to solve we let y=z^α |

What method do you use for this equation y''(x)+a(x) y'(x)+b(x)y=c(x) where a(x) and b(x) are constants and c(x)=0 ? | Assume y(x)=e^mx and make a quadratic equation then solve for each case. |

What is the form and name of the equation when a^2-4b>0 ? | Over damped and y(x)=c_1 e^(m_1 x)+c_2 e^(m_2 x) |

What is the form and name of the equation when a^2-4b=0 ? | Critical damping and y(x)=[c_1 x+c_2 ] e^mx |

What is the form and name of the equation when a^2-4b<0 ? | Under damped and y(x)=e^αx [Acos(βx)+Bsin(βx)] |

What method do you use for this equation dy/dx=b(x)/g(y) where g(y) is of the form (ay+k)^(-1)? | We take the equation in the separation of variables form y(x)=1/a(ce^(∫ab(x)dx)-k) |