Solve the differential equation yeyxdx=(xeyx+y2)dy(y=0)
Number of values of m∈N for which y=emx is a solution of the differential equation dx3d3y−3dx2d2y−4dxdy+12y=0 (a) 0 (b) 1 (c) 2 (d) More than 2
A cyclist moving on a level road at 4 m/s stops pedalling and lets the wheels come to rest. The retardation of the cycle has two components: a constant 0.08 m/s2 due to friction in the working parts and a resistance of 0.02v2/m , where v is speed in meters per second. What distance is traversed by the cycle before it comes to rest? (consider 1n 5=1.61).
The differential equation dxdy=y1−y2 determines a family of circle with (a) variable radii and a fixed centre at(0,1) (b) variable radii and a fixed centre at (0,−1)(c) Fixed radius 1 and variable centres along the x-axis. (d) Fixed radius 1 and variable centres along the y-axis.
The slope of the tangent at (x,y) to a curve passing through (1,4π) is given by xy−cos2(xy), then the equation of the curve is
Statement 1 : Degree of the differential equation 2x−3y+2=log(dxdy) is not defined. Statement 2 : In the given differential equation, the power of highest order derivative when expressed as the polynomials of derivatives is called degree.