Find the equation of the family of curves whose slope at any...

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00:01 Hello students, in the question we are asked to find the equation of family of curve whose slopes are.

00:06 So we have four parts.

00:08 In part a, a slope is 3x square plus 4.

00:12 So we know that d divided by dx is equals to 3x square plus 4.

00:19 So now separating this, we get dy is equal to 3x square plus 4 multiplied by dx.

00:26 Now integrating both sides, integrating both sides, we get integration d ,y is equal to integration 3x square plus 4 multiplied by dx.

00:46 So solving this, we get y is equal to 3x cubed divided by 3 plus 4x plus c.

00:53 So from here we get y is equal to x q plus 4x plus c.

00:59 So this is our equation of family of curve.

01:03 Now in part b, in part b we are given x divided by y.

01:08 So our equation will be dyy d x is equals to x divided by y.

01:14 Separating terms we get y -d -y is equal to x -tx.

01:18 Now integrating both sides, integrating, integrating, integrating both sides, both sides, we get integration y, d ,y is equals to integration x, dx.

01:36 So, solving this, we get, solving this, we get y squared divided by 2 is equals to x square divided by 2 plus c.

01:45 So from here, we get the equation y square is equal to x square plus 2c.

01:52 So this is our equation...

Question

Find the equation of the family of curves whose slope at any point (x, y) is 1. 3x^2 + 4 2. x / y 3. (x + 1) / (y - 1) 4. equal to the square root of the abscissa of the point.

Question

Find the equation of the family of curves whose slope at any point (x, y) is 1. 3x^2 + 4 2. x / y 3. (x + 1) / (y - 1) 4. equal to the square root of the abscissa of the point.

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