The integrating factor of differential equation xdy/dx + 2y = x^2 x is Option 1: 1/x Option 2: x Option 3: 1/x^2 Option 4: x^2

Answer: x^2. Solution: Convert to standard form by dividing by x: dy/dx + 2/x y = x x. Here P(x) = 2/x. Integrating factor = e^( (2/x) dx) = e^(2 x) = x^2.

Calculus

Differential Equations

Easy

The integrating factor of differential equation $x\frac{dy}{dx} + 2y = x^2 \log x$ is

$\frac{1}{x}$

$x$

$\frac{1}{x^2}$

$x^2$

✅ Correct Option: 4

Convert to standard form by dividing by $x$ : $\frac{dy}{dx} + \frac{2}{x} y = x \log x$ . Here $P(x) = 2/x$ . Integrating factor $= e^{\int (2/x) dx} = e^{2 \ln x} = x^2$ .

2023: 15 June Shift 2

The differential equation whose solution is $Ax^2 + By^2 = 1$ where A and B are arbitrary constant is of :

(A) first order and first degree

(B) second order and first degree

(D) second order

Choose the correct answer from the options given below :

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[where c is an arbitrary constant]

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The solution of the differential equation $\frac{dy}{dx} = x^2 + x + \frac{1}{x}$ is

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Solution of differential equation $\frac{dy}{dx} = e^{x+y} - xe^y$ is

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If $U(x) = x + \sqrt{1 + x^2}$ , then solution of the differential equation $\frac{dy}{dx} + \sqrt{\frac{1 + y^2}{1 + x^2}} = 0$ , is :

The integrating factor of differential equation xdydx+2y=x2log⁡xx\frac{dy}{dx} + 2y = x^2 \log xxdxdy​+2y=x2logx is

Solution

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CUET Mathematics Past Year Questions (Topic-Wise)

The integrating factor of differential equation $x\frac{dy}{dx} + 2y = x^2 \log x$ is