Classifying a Differential Equation

Calculus Level 1

∂ 2 x ∂ t 2 + t x = ∂ y ∂ t \frac{\partial ^2 x}{\partial t^2}+tx=\frac{\partial y}{\partial t}

Which of the following best describes the above equation?

Non-linear partial second-order Linear partial second-order Linear partial first-order Non-linear partial first-order

Samir Khan by Samir Khan , 23, USA

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2 solutions

Samir Khan
Jun 12, 2016

The equation contains a second derivative, so it is second-order. There are no terms involving a derivative multiplied by a function, or a derivative raised to a power, so the equation is linear.

7 Helpful 1 Interesting 0 Brilliant 0 Confused

Are you sure about the partial part? It says: "[...] a partial differential equation is one involving derivatives with respect to multiple variables". However, all derivatives are taken wrt a single variable, t.

Simon Böhm - 4 months, 3 weeks ago
Sumanth Lazarus
Mar 14, 2018

This is linear because of the each term is linear term of variable x and y i.e partially nth derivative of respective variable in isolation. Partial because the function is dependent on two variable x, y. Second order because highest power of derivative is 2.

1 Helpful 0 Interesting 0 Brilliant 0 Confused

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