OF THE INDEPENDENT VARIABLE. 189 



m f d*y 2x dy y . . . 



2. Iransform -r^ + ^ - 2 ~r + , 2x2 = into an equa- 



dx 1+x ax (1 + x ) 



tion in which 6 is the independent variable, where 

 6 = tsaor l x. _ T d*y 



Result ^ + y = - 



3. Transform -^ + - -- + y = 0, into an equation in which 



t is the independent variable where y? = U. 



5. If a? = cosi, then 



G. Transform j f ^ ^ , by assuming x r cos 0, 



Result 



7. If x = r cos 0, y = r sin 0, shew that 



dy 



Idr 



8. If a; = a (1 - cos <) and y = a (w< + sin ), express 



n cos < + 1 



r , 7j 



jr3 in terms of t. Result -- . 



cte a sin 



. 8 



