Integrating factor of the differential equation (1 - y^2)dx/dy + xy = ay is : Option 1: 1/(1 - y^2) Option 2: 1/(√(y^2 - 1)) Option 3: 1/(y^2 - 1) Option 4: 1/(√(1 - y^2))

Answer: 1/(√(1 - y^2)). Solution: Standard form: dx/dy + y/(1-y^2)x = ay/(1-y^2). IF = e^( y/(1-y^2)dy) = e^(-1/2, 1-y^2, ) = 1/(√(1-y^2)).

Calculus

Differential Equations

Medium

core

Integrating factor of the differential equation $(1 - y^2)\frac{dx}{dy} + xy = ay$ is :

$\frac{1}{1 - y^2}$

$\frac{1}{\sqrt{y^2 - 1}}$

$\frac{1}{y^2 - 1}$

$\frac{1}{\sqrt{1 - y^2}}$

✅ Correct Option: 4

Standard form: $\frac{dx}{dy} + \frac{y}{1-y^2}x = \frac{ay}{1-y^2}$ .

$IF = e^{\int \frac{y}{1-y^2}dy} = e^{-\frac{1}{2}\ln|1-y^2|} = \frac{1}{\sqrt{1-y^2}}$ .

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Integrating factor of the differential equation (1−y2)dxdy+xy=ay(1 - y^2)\frac{dx}{dy} + xy = ay(1−y2)dydx​+xy=ay is :

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Integrating factor of the differential equation $(1 - y^2)\frac{dx}{dy} + xy = ay$ is :