المحلولة بالنسبة للمتحول x

الكاتب Muhanad

المعادلة التفاضلية^[م] العادية المحلولة بالنسبة للمتحول وشكلها العام $x = f(y')$

لحل هذه المعادلة نفرض أنّ $y' = t\quad$

وبالتالي يكون:

$\begin{array}{l}\\\left.\begin{array}{l}x = f(y')\\\\y' = t\\\end{array}\right\}\quad\Rightarrow\quad \\ \\ x = f(t)\quad\Rightarrow\quad dx = f'(t)dt\\\\y =\int {y'dx\; =\;\int {t\;.\;f'(t)\;} } dt\\\end{array}$

وبالتالي الحل العام يعطى على الشكل التالي:

$\boxed{\;\;\;\;\begin{array}{l}x = f(t)\\\\y = \int {t.f'(t).dt + c}\\ \end{array}\;\;\;\;}$

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Muhanad مشرف في الرياضيات رمز

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