기록

1. Homogeneous Linear ODE of Second Order $y''+p(x)y'+q(x)y=r(x)\left\{\begin{matrix} r=0 (homo) \\ r\neq 0 (non-homo) \end{matrix}\right.$ $L=\frac{\mathrm{d}^{2} }{\mathrm{d} x^{2}}+p\frac{\mathrm{d} }{\mathrm{d} x}+q$ $L(y)=r(x)$ $L(\alpha y_{1}+\beta y_{2})=(\alpha y_{1}+\beta y_{2})''+p(\alpha y_{1}+\beta y_{2})'+q(\alpha y_{1}+\beta y_{2})$ $ =\alpha y_{1}''+\beta y_{2}''+p\alpha y..

6. Linear $f(\alpha x+\beta y)=\alpha f(x)+\beta f(y)$: Linear $y'+p(x)y=r(x) \left\{\begin{matrix} r=0 (homo)\\ r\neq 0 (non-homo) \end{matrix}\right.$ $L=\frac{\mathrm{d} }{\mathrm{d} x}+p$ $L(y)=r(x)$ $L(\alpha y_{1}+\beta y_{2})=\frac{\mathrm{d} }{\mathrm{d} x}(\alpha y_{1}+\beta y_{2})+p(\alpha y_{1}+\beta y_{2})=\alpha y_{1}'+\beta y_{2}'+p\alpha y_{1}+p\beta y_{2}$ $ =\alpha (y_..

Ordinary Differential Equation 카테고리는 10th (Erwin Kreyszig)의 순서를 따라갑니다 1. Basic Concepts Physical System → Mathematical Model → Mathematical Solution → Physical Interpretation Ordinary Differential Equation Order(n) First-Order ODE: $F(x,y,y')=0, y'=f(x,y)$ General Solution: containing an arbitrary constant c Particular Solution: not containing an arbitrary constant c Initial Value Problem: $ y..