It can be helpful to classify a differential equation, so that we can predict th

Question

It can be helpful to classify a differential equation, so that we can predict the techniques that might help us to find a function which solves the equation. The most common classifications are based on: the order of the equation whether the equation is linear or nonlinear whether the equation is homogeneous or non-homogeneous. The order of an equation is given by the highest number of derivatives involved. Linearity is important because the structure of the family of solutions to a linear equation is fairly simple. Linear equations can usually be solved completely and explicitly. Homogeneous equations are easier to solve and the solution of a non-homogeneous equation has as component the solution to the corresponding homogeneous equation. Classify the following equations: 5t^-1 d^2y/dt^2 - t^2 dy/dt + 2y = 0 t^2 d^2y/dt^2 + t dy/dt + 2y = sin t y" - y + t^2 = 0 d^4y/dt^4 - 5 d^3y/dt^3 + 4 d^2y/dt^2 + dy/dt = y y" = ty" + Squareroot ty" + 5y (1 + y^2) d^2y/dt^2 + t dy/dt + y = e^t

Explanation / Answer

1. Second order linear homogeneous.

2. Second order linear non-homogeneous.

3. Second order linear non-homogeneous.

4. Fourth order linear homogeneous.

5. Third order linear homogeneous.

6. Second order non-linear non-homogeneous.

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