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The general solution of `x(dy)/(dx)=y-x tan(y/x)` is ……. .A. `x^(2)sin(x/y)=c`B. `xsin(x/y)=c`C. `xsin(y/x)=c`D. `x^(2)sin(y/x)=c` |
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Answer» Correct Answer - C We have,x`(dy)/(dx)=y-xtan(y/x)` `rArr(dy)/(dx)=y/x-tan(y/x)` Put `y/x=vrArry=vx` `rArr(dy)/(dx)=v+x(dv)/(dx)` `thereforev+x(dv)/(dx)=v-tanv` `rArrx(dv)/(dx)=-tanv` `rArrcotvdv=-(dx)/x` `rArrlog(sinvdotx)=logc` `rArrsin(y/x)dotx=c` `rArrxsin(y/x)=c` |
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