Questions in diff-equation

Select	Question
	A particle moves in a straight line with a velocity given by $\frac{dx}{dt}=x+1$(x is the distance described). The time taken by a particle to traverse a distance of 99 metre is
	Solution of differential equation $x\,dy-y\,dx=0$ represents
	Integral curve satisfying $y'=\frac{{{x}^{2}}+{{y}^{2}}}{{{x}^{2}}-{{y}^{2}}},\ y(1)=2$ has the slope at the point (1, 0) of the curve, equal to
	A particle starts at the origin and moves along the x–axis in such a way that its velocity at the point (x, 0) is given by the formula $\frac{dx}{dt}={{\cos }^{2}}\pi x.$ Then the particle never reaches the point on
	The slope of the tangent at (x, y) to a curve passing through a point (2, 1) is $\frac{{{x}^{2}}+{{y}^{2}}}{2xy}$, then the equation of the curve is
	A function $y=f(x)$ has a second order derivatives ${{f}'}'(x)=6(x-1)$. If its graph passes through the point (2, 1) and at that point the tangent to the graph is $y=3x-5$, then the function is
	The solution of the differential equation $x\frac{{{d}^{2}}y}{d{{x}^{2}}}=1$, given that $y=1,\ \frac{dy}{dx}=0$when $x=1$, is
	The solution of the differential equation $\frac{{{d}^{2}}y}{d{{x}^{2}}}=-\frac{1}{{{x}^{2}}}$ is
	The solution of the differential equation ${{\cos }^{2}}x\frac{{{d}^{2}}y}{d{{x}^{2}}}=1$ is
	The solution of $\frac{{{d}^{2}}y}{d{{x}^{2}}}={{\sec }^{2}}x+x{{e}^{x}}$is