Find the general solution of the differential equations dxdy=4−y2 , (−2<y<2)
Identify the statement(s) which is/are true. (a) f(x,y)=exy+xtany is a homogeneous of degree zero. (b)xxlnydx+xy2⋅sin−1(xy)dy=0 is a homogeneous differential equation. (c)f(x,y)=x2+sinxcosy is a non homogeneous. (d)(x2+y2)dx−(xy2−y3)dy=0 is a homogeneous differential equation.
Form the differential equation of all circles touching the x-axis at the origin and center on y-axis.
If y1 and y2 are the solution of the differential equation dxdy+Py=Q , where P and Q are functions of x alone and y2=y1z , then prove that z=1+⋅e−fy1Qdx, where c is an arbitrary constant.