If integrating factor of x ( 1 − x 2 ) d y + ( 2 x 2 y − y − a x 3 ) d x = 0 is e ∫ P d x , then P is equal to Options: A . &nbsp 2 x 2 − a x 3 x ( 1 − x 2 ) B . &nbsp ( 2 x 2 − 1 ) C . &nbsp 2 x 2 − 1 a x 3 D . &nbsp ( 2 x 2 − 1 ) x ( 1 − x 2 )

Answer: Option D : D x ( 1 − x 2 ) d y + ( 2 x 2 y − y − a x 3 ) d x = 0 d y d x + ( 2 x 2 − 1 ) x ( 1 − x 2 ) y = a x 2 ( 1 − x 2 ) , ∴ P = 2 x 2 − 1 x ( 1 − x 2 ) .

If integrating factor of x(1−x2)dy+(2x2y−y−ax3)dx=0 is e&

Discussion Forum : Differential Equations

Question -

If integrating factor of $x (1 - x^{2}) d y + (2 x^{2} y - y - a x^{3}) d x = 0$ is $e^{\int P d x}$ , then P is equal to

Options:

A .

\frac{2 x^{2} - a x^{3}}{x (1 - x^{2})}

B .

(2 x^{2} - 1)

C .

\frac{2 x^{2} - 1}{a x^{3}}

D .

\frac{(2 x^{2} - 1)}{x (1 - x^{2})}

Answer: Option D
:
D

x (1 - x^{2}) d y + (2 x^{2} y - y - a x^{3}) d x = 0 \frac{d y}{d x} + \frac{(2 x^{2} - 1)}{x (1 - x^{2})} y = \frac{a x^{2}}{(1 - x^{2})}, ∴ P = \frac{2 x^{2} - 1}{x (1 - x^{2})}

Was this answer helpful ?

Next Question

Discussion Forum : Differential Equations

Submit Your Solution hear: