Match List – I with List – II. List - I Differential equation List - II Integrating Factor (I.F.) Choose the correct answer from the options given below:(A) \(\frac{dy}{dx} - \frac{y}{x} = 2x\) (I) \(x^{2} - 1\) (B) \(\frac{dy}{dx} + \left( \frac{2x}{x^2 - 1} \right) y = \frac{2}{(x^2 - 1)^2}\) (II) \(\sqrt{ x^{2}-1 }\) (C) \(\frac{dy}{dx} - \big( \frac{x}{1- x^{2} } )y= \frac{1}{ 1-x^{2} }\) (III) \(\frac{1}{x}\) (D) \(\frac{dy}{dx} + \frac{y}{1 + x^2} = \frac{cotx}{1+ x^{2} }\) (IV) \(1+ x^{2}\)
(A) \(\frac{dy}{dx} - \frac{y}{x} = 2x\)
Integrating factor = \(e^{\int -\frac{1}{x} dx} = e^{-\log x} = \frac{1}{x}\)
(B) We have
\(\frac{dy}{dx} + \left( \frac{2x}{x^2 - 1} \right) y = \frac{2}{(x^2 - 1)^2}\)
Integrating factor = \(e^{\int \frac{2x}{x^2 - 1} dx} = e^{\log(x^2 - 1)} = x^2 - 1\)
(C) \(\frac{dy}{dx} - \big( \frac{x}{1- x^{2} } )y= \frac{1}{ 1-x^{2} }\)
Integrating factor = \(e^{-\int \frac{1}{(1-x^2 )} dx} = \sqrt{1 - x^2}\)
(D) \(\frac{dy}{dx} + \frac{y}{1 + x^2} = \frac{cotx}{1+ x^{2} }\)
Integrating factor = \(e^{\int \frac{2x}{1 + x^2} dx} = e^{\int \log(1 + x^2)} = 1 + x^2\)
Important Questions from Mixed Topics (CUET-UG)
- The area of the region bounded by y=|x-5|, x=0 and x=1 is:
The equation of the normal to the curve \(y = 4x^3 + 2 \sin(x)\) at \((0, 3)\)
\(y = 4x^3 + 2 \sin(x)\) at \( (0, 3) \)
Which of the following statement is incorrect?
Which of the following statement is TRUE?
Which of the following statement is correct?
