InterviewSolution
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InterviewSolution
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`x^(2)(dy)/(dx)=x^(2)-2y^(2)+xy` |
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Answer» `x^(2)dy-(x^(2)+xy-2y^(2))dx=0` `implies (dy)/(dx)=(x^(2)+xy-2y^(2))/(x^(2))` `implies v+x(dv)/(dx)=(x^(2)+x^(2)v-2x^(2)v^(2))/(x^(2))` `=1+v-2v^(2)` `implies x(dv)/(dx)=1-2v^(2)` माना `y = vx implies (dy)/(dx)=v+x(dv)/(dx)` `implies (dv)/(1-2v^(2))=(dx)/(x)` `implies (1)/(2)int(1)/(((1)/sqrt(2))^(2)-v^(2))dv=int(dx)/(x)+c` `=(1)/(2).(1)/(2.(1)/(sqrt(2)))log.((1)/(sqrt(2))+v)/((1)/(sqrt(2))-v)=logx+c` `implies (1)/(2sqrt(2))log.(1+vsqrt(2))/(1-vsqrt(2))=logx+c` `implies (1)/(2sqrt(2))log.(1+(y)/(x)sqrt(2))/(1-(y)/(x)sqrt(2))=log x+c` `implies (1)/(2sqrt(2))log.(x+ysqrt(2))/(x-ysqrt(2))=logx+c` |
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