sir i only need the correct option

### Asked by arijits949596 | 29th Apr, 2020, 10:26: PM

Expert Answer:

### Correct option for each of the questions:
1. The slope at point of a curve y=f(x) is given by dy/dx=3x^{2} and it passes through (-1, 1). The equation of the curve is x^{3}+2.
2. Degree of the differential equation [1+(dy/dx)^2]^5/3 = d^{2}y/dx^{2} is 1.
3. The general solution of the differential equation d^{2}y/dx^{2}=e^{-2x} is y=1/4 e^{-2x} +cx +d.
4. The differential equation of the family of all circles with centre at origin is x+yy_{1}=0
5. The solution of the differential equationdy/dx=e^{x+y} + e^{y-x} is e^{-y} = e^{-x} - e^{x} + c.
6. Differential equation of all tangents to the parabola y^2=4ax is y=mx+a/m.
7. The differential equation satisfied by y = A/x + B is xy_{2}+2y_{1}=0.
8. The equation of the curve whose slope at any point different from origin is y+y/x is y = xe^x + c, c is not equal to zero.
9. Solution of the differential equation dy/dx = 1+xy is ye^{(-x^2)/2} = {e^{(-x^2)/2}}/-x+c
10. The general solution of the differential equation (d^{2}y/dx^{2})2+(dy/dx)^{2}-xy=0 is
11. The integrating factor of the differential equation dy/dx(xlox)+y=2logx is given by log x.
12. Solution of the differential equation dy/dx+y/x = x^{2} is given by y=1/4 x^{3} + cx^{-1}, c is any real number.

^{2}and it passes through (-1, 1). The equation of the curve is x

^{3}+2.

^{2}y/dx

^{2}is 1.

^{2}y/dx

^{2}=e

^{-2x}is y=1/4 e

^{-2x}+cx +d.

_{1}=0

^{x+y}+ e

^{y-x}is e

^{-y}= e

^{-x}- e

^{x}+ c.

_{2}+2y

_{1}=0.

^{(-x^2)/2}= {e

^{(-x^2)/2}}/-x+c

^{2}y/dx

^{2})2+(dy/dx)

^{2}-xy=0 is

^{2}is given by y=1/4 x

^{3}+ cx

^{-1}, c is any real number.

### Answered by Renu Varma | 30th Apr, 2020, 01:59: PM

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