อ้างอิง:
|
จงหาผลเฉลยของ $\frac{dy}{dx}+25xy=9.8 ; y(0)=2$
|
$y=e^{-{\int p(x)dx}}(\int q(x)e^{\int p(x)dx}dx+c)$
$=e^{-25x^2/2}(\int_0^x9.8e^{25t^2/2}dt+c)$
$y(0) = 2\Rightarrow c=2$
$y=9.8e^{-25x^2/2}\int_0^xe^{25t^2/2}dt+2e^{-25x^2/2}$
We must keep the integral term if we don't know the closed form krub.