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    				| 1. | Solve the different equation : `x+y(dy)/(dx)=sec(x^(2)+y^(2))`. Also find the particular solution if x=y=0. | 
| Answer» The given differential equation is, `x+y(dy)/(dx)=sec(x^(2)+y^(2))` . . . (i) Let `x^(2)+y^(2)=t` `2x+2y(dy)/(dx)=(dt)/(dx)` `2(x+y(dy)/(dx))=(dt)/(dx)` `x+y(dy)/(dx)=(1)/(2)(dt)/(dx)` From equation (i) , `(1)/(2)(dt)/(dx)=sect` `int(dt)/(sect)=int2dx` `intcostdt=2x+c` `sint=2x+c` `sin(x^(2)+y^(2))=2x+c` When x =0, y=0, we have `sin0=0+c` c=0 `therefore` The particular solution is given by, `sin(x^(2)+y^(2))=2x` | |