Differential Equation

Study Material (PDF)
Self Assesment
Study Material (PDF)
Self Assesment

Click on each question to see answer & solution.

Question No: #161

The slope of a curve at point `(x,y)` is `\frac{x^2+y^2}{2xy}` and the curve passing through the point `(1,0)`. Find the equation of curve.
Ans: `x^2-y^2=x`
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Question No: #162

Show that the equation of the curve, passing through the point `(1,0)` and satisfying the differential equation `(1+y^2)dx+xy\dy=0` is `x^2-y^2=1`

Question No: #163

A particle is moving with velocity `u` through a straight line and its acceleration is equal to its displacement. At an instant, if displacement be `x` and velocity be `v`, then prove that `v^2=u^2+x^2`

Question No: #164

Find the differential equation of all parabolas, whose axes are along `y`-axis and vertices are at origin.

Question No: #165

A point is moving through a parabolic curve `y^2=4x`. At which point abscissa increases at twice the rate the ordinate increases?

Question No: #166

A point moves through a curve `6y=x^3+2`. At which point ordinate increases at 8 times the rate of abscissa increases?

Question No: #167

If the rate of change of area of a circle is equal to rate of change of its diameter, then radius of the circle is -- (i) `\frac{2}{\pi}`, (ii) `\frac{1}{\pi}`, (iii) `\frac{\pi}{2}`, (iv) `\pi`

Question No: #168

If the area of a circle increases uniformly with respect to time, then show that the rate of increment of its circumference is inversely proportional to its radius.

Question No: #169

If the circumference of a circle increases uniformly, then show that the rate of increment of its area is proportional to its radius.

Question No: #170

A circular ink drop increases at a rate of 2 square cm per second. Find the rate of change of its radius at time `2\frac{6}{11}` sec.