The expression which is the general solution of the differential e | Filo

Class 12

Math

Calculus

Differential Equations

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The expression which is the general solution of the differential equation dydx+x1−x2y=xy√ is

1. y√+13(1−x2)=c(1−x2)14
2. y(1−x2)14=c(1−x2)
3. y√(1−x2)14=13(1−x2)+c
4. None of these
Solution: [a] Divide the equation by y√, we getPut y12=z⇒12y−12dydx=dzdxI. F. e∫12[x1−x2]dx=e−14log(1−x2)=(1−x2)14is z(1−x2)−14=∫x2(1−x)−14dx+c⇒y√(1−x2)14=12(−12)(1−x2)3/43/4+c⇒y√+13(1−x2)=c(1−x2)14
608
150

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