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what is the definition of a linear differential equation. Such equations are physically suitable for describing various linear phenomena in biology economics population dynamics and physics. In this case unlike most of the first order cases that we will look at we can actually derive a formula for the general solution.
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Appears in the equation raised to the power of 1 or 0 has coefficients which are either functions of the independent variable like time or constants. A linear equation or polynomial with one or more terms consisting of the derivatives of the dependent variable with respect to one or more independent variables is known as a linear differential equation. Its solution set will coincide with KerL.
If the dependent variable and all its partial derivatives occur linearly in any PDE then such an equation is called linear PDE otherwise a nonlinear PDE.
This is also true for a linear equation of order one with non-constant coefficients. The dimension of the. Most ODEs that are encountered in physics are linear. In particular the kernel of a linear transformation is a subspace of its domain.
