Continuity and Differentiability
If x and y are connected parametrically by the equations given, without eliminating the parameter, Find dxdy.x=2at2,y=at4
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Find the particular solution of the differential equation xexy−y+xdxdy=0 given that y(e)=0.
Find the general solution for the following differential equation.xdxdy+y=3x2−2,x>0
The general solution of the D.E. dxdy+ytanx=secx is
Find the general solution of the following differential equations:dxdy=y+2x−1
y=x2+cosxFind a particular solution satisfying the given condition for the following differential equation.dxdy+ytanx=2x+x2tanx, given that y=1 when x=0.
Verify the Mean Value Theorm for f(x)=x2 in the interval [2,4].
Find the equation of a curve which passes through the origin and whose differential equation is dxdy=exsinx.
Find the general solution for the following differential equation.xdxdy+2y=x2logx