Question

linear second order ordinary differential equation is non homogeneous if

Answer 1

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So, thé answer is --) Each such nonhomogeneous equationhas a corresponding homogeneous equation: y″ + p(t)y′ + q(t)y = 0. ... We will focus our attention to the simpler topic of nonhomogeneous second order linear equations with constant coefficients: ay″ + by′ + cy = g(t).

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Answer 2

Answer:

Concept:

You must first be familiar with the characteristics of a homogeneous differential equation in order to recognize a nonhomogeneous differential equation. Additionally, you frequently have to resolve one before resolving the other.

Step-by-step explanation:

Similar to homogeneous differential equations, nonhomogeneous differential equations can also have terms on the right side that involve solely x (and constants), as in the following equation:

                              $\frac{d^{4} y}{d x^{4}}+x \frac{d^{2} y}{d x^{2}}+y^{2}=6 x+3$

You also can write nonhomogeneous differential equations in this format: $y^{\prime \prime}+p(x) y^{\prime}+ q(x) y=g(x)$. The general solution of this nonhomogeneous differential equation is

                            $y=c_{1} y_{1}(x)+c_{2} y_{2}(x)+y_{p}(x)$

In this solution, $c_{1} y_{1}(x)+c_{2} y_{2}(x)$  is the general solution of the corresponding homogeneous differential equation:

                             $y^{\prime \prime}+p(x) y^{\prime}+q(x) y=0$

And  $y_{p}(x)$ is a specific solution to the nonhomogeneous equation.

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