If integrating factor of x1-x2dy-2x2y-y-ax3dx-0 is e-P dx- then P is equal to-

X(1 x^2)dy+(2x^2y y ax^3)dx=0 ⇒ x(1 x^2)dydx+2x^2y y ax^3=0 ⇒ x(1 x^2)dydx+y(2x^2 1)=ax^3 ⇒dydx+2x^2 1x(1 x^2)y=ax^3x(1 x^2) Which is of the form dydx+Py=Q. It ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Mathematics

Integrating Factor

If integratin...

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:

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

No worries! We‘ve got your back. Try BYJU‘S free classes today!

2 x^{3} - 1

No worries! We‘ve got your back. Try BYJU‘S free classes today!

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

No worries! We‘ve got your back. Try BYJU‘S free classes today!

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

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

Open in App

Solution

The correct option is D $\frac{2 x^{2} - 1}{x (1 - x^{2})}$
$x (1 - x^{2}) d y + (2 x^{2} y - y - a x^{3}) d x = 0$
$\Rightarrow x (1 - x^{2}) \frac{d y}{d x} + 2 x^{2} y - y - a x^{3} = 0$
$\Rightarrow x (1 - x^{2}) \frac{d y}{d x} + y (2 x^{2} - 1) = a x^{3}$
$\Rightarrow \frac{d y}{d x} + \frac{2 x^{2} - 1}{x (1 - x^{2})} y = \frac{a x^{3}}{x (1 - x^{2})}$

Which is of the form $\frac{d y}{d x} + P y = Q .$
Its integrating factor is $e^{\int P d x},$ where
$P = \frac{2 x^{2} - 1}{x (1 - x^{2})}$

Suggest Corrections

Similar questions

Q. If integrating factor of

x (1 - x^{2}) d y + (2 x^{2} y - y - a x^{3}) d x = 0

e^{\int P d x}

, then P is equal to

Q. For the differential equation

x (1 - x^{2}) d y + (2 x^{2} y - y - a x^{3}) d x = 0.

If y(1)=0 then the value of the constant is

Q. Solve

x (1 - x^{2}) d y + (2 x^{2} y - y - 5 x^{3}) d x = 0

Q. The integrating factor of the differential equation

(1 + x^{2}) \frac{d y}{d x} + y = x

Q. The integrating factor of the differential equation

(1 + x^{2}) \frac{d y}{d x} + y = e^{{tan}^{- 1} x}

is:

Join BYJU'S Learning Program

Explore more

Integrating Factor

Standard XII Mathematics

Join BYJU'S Learning Program

If integrating factor of x(1−x2)dy+(2x2y−y−ax3)dx=0 is e∫Pdx, then P is equal to:

The correct option is D 2x2−1x(1−x2)x(1−x2)dy+(2x2y−y−ax3)dx=0 ⇒x(1−x2)dydx+2x2y−y−ax3=0 ⇒x(1−x2)dydx+y(2x2−1)=ax3 ⇒dydx+2x2−1x(1−x2)y=ax3x(1−x2) Which is of the form dydx+Py=Q. Its integrating factor is e∫Pdx, where P=2x2−1x(1−x2)

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: