INTEGRAL CALCULUS. -Jl: 



lies on a fixed circle; and obtain the general integral and singular 

 solution. 



1053. Along the normal to a curve at P is measured a con- 

 li'iijjth PQy is a fixed point and the curve is such that 



the circle described al>out OPQ has a fixed tangent at ; find the 

 differential equation of the curve, the general integral, and sin- 

 gular solution. 



1054. If PJ/, PG be the ordinate and normal from a point P 

 of a curve to the axis of #, find a curve (1) in which PJ/ 2 varies 



PM* 

 as PG', (2) in which the curvature varies as ' : and pn.v<- 



that one species of curve satisfies both conditions. 



1055. Find the orthogonal trajectory of the circles 



X being the parameter. 



105G. Integrate the equations : 



( 2 ) - 



(3) j+ 



(4) 2*y*-^ +2V * f 



' dxdy y dx dx 9 dy 



(5) ^.-a^+iM/.a 



1057. The general solution of the equation 



IS 



