The equation of the curve satisfying the differential equation $y_{2} (x^{2} + 1) = 2 x y_{1}$ passing through the point $(0, 1)$ and having slope of tangent at $x = 0$ as $3$ is:

y = x^{2} + 3 x + 2

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

y^{2} = x^{2} + 3 x + 1

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

y = x^{2} + 3 x + 1

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

n o n e o f t h e s e

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

Open in App

Solution

The correct option is B $y = x^{2} + 3 x + 2$
The given differential equation can be written as $y_{2} / y_{1} = 2 x / (x^{2} + 1)$ .
Integrating both the sides we have $log y_{1} = log (x^{2} + 1) + C$ , which implies $log y_{1} (0) = log 1 + C$ , i.e., $C = log 3$ . Therefore,
$log y_{1} = log (x^{2} + 1) + log 3$ which implies
$y_{1} = 3 (x^{2} + 1)$ or $y = x^{3} + 3 x + A$ , so $1 = y (0) = 0 + 0 + A$ , i.e., $A = 1$ . Hence the required
equation of curve is $y = x^{3} + 3 x + 1$ .

Suggest Corrections

Similar questions

Q. The equation of the curve satisfying the differential equation

y^{^{''}} (x^{2} + 1) = 4 x y^{^{'}}

, passing through the point

(0, - 4)

and having slope of the tangent at

x = 0

4

Q. The equation of curve passing through (3, 4) and satisfying the differential equation

y {(\frac{d y}{d x})}^{2} + (x - y) \frac{d y}{d x} - x = 0

can be

Q. The equation of one of the curve passing through

(1, 4)

and satisfying the differential equation

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

The equation of the curves, satisfying the differential equation $\frac{d^{2} y}{d x^{2}} (x^{2} + 1) = 2 x \frac{d y}{d x}$ passing through the point $(0, 1)$ and having the slope of tangent at $x = 0$ as $6$ is

Q. The equation of the circle concentric with x² + y² − 3x + 4y − c = 0 and passing through (−1, −2) is
(a) x² + y² − 3x + 4y − 1 = 0
(b) x² + y² − 3x + 4y = 0
(c) x² + y² − 3x + 4y + 2 = 0
(d) none of these

Join BYJU'S Learning Program

The equation of the curve satisfying the differential equation y2(x2+1)=2xy1 passing through the point (0,1) and having slope of tangent at x=0 as 3 is:

The equation of the curve satisfying the differential equation $y_{2} (x^{2} + 1) = 2 x y_{1}$ passing through the point $(0, 1)$ and having slope of tangent at $x = 0$ as $3$ is: