Find the general solution of the differential equation dxdy−y=cosx
Show that the given differential equation is homogeneous and solve each of them.xdxdy−y+xsin(xy)=0
Verify that the given functions (explicit or implicit) is a solution of the corresponding differential equation:ycosy=x : (y sin y + cos y + x) y = y
A homogeneous differential equation of the from dydx=h(yx)can be solved by making the substitution.(A) y=vx (B) v=yx (C) x=vy (D) x=v
Form the differential equation of the family of circles in the second quadrant and touching the coordinate axes.
Verify that the function y=c1eaxcosbx+c2eaxsinbx, where c1,c2are arbitrary constants is a solution of the differential equation. dx2d2y−2adxdy+(a2+b2)y=0
Find the equation of a curve passing through the point (2,3), given that the slope of the tangent to the curve at any point (x, y) is y22x.