معادلة فيها x, y, y', y'', y''', ……
1- Homogeneous D.E :
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مراجعة
التكاملات
1- ∫
du / √ a2 – u2 = sin-1 u / a
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الصورة العامة - y' = F(x,y)
or
M(x,y)dx + N(x,y)dy = 0
1- Separable equations :
ويتم فيها فصل x عن y (فصل المتغيرات)
to solve the separable equation :
1. set y' = dy/dx
dy/dx = f(x)g(y)
2. dy/g(y) = f(x)dx
3. by integration we obtain the solution .
:: Special case ::
- If the DE in the form y' = F ( ax + by + c )
to solve this equation we set [ ax + by + c = z ]
2- Homogeneous equations :
F(x,y) is called homogeneous of degree if F( tx, ty ) = tn F(x,y)
إذا كان كل حد من حدود المعادلة من نفس الدرجة تبقى homogeneous
or x/y or y/x
a DE M(x,y)dx + N(x,y)dy = 0
is called homogeneous if M(x,y) & N(x,y) are hom
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