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Mp Raju 5 years, 6 months ago
given d.e
xdx-yey{tex}\sqrt{1+x^2} {/tex}dy=0
both sides divided by {tex}\sqrt{1+x^2}{/tex}
{tex}\implies {/tex}{tex}\frac{x}{\sqrt{1+x^2}} {/tex}dx-y ey dy=0
{tex}\implies {/tex}{tex}\int{/tex} {tex}\frac{x}{\sqrt{1+x^2}}dx-\int y e^y dy =0 {/tex}
{tex}\implies {/tex}{tex}\sqrt{1+x^2}{/tex} - yey+ey=c
at (0,1)
{tex}\implies{/tex}1-e+e=c
{tex}\implies{/tex}c=1
particular solution is {tex}\sqrt{1+x^2}{/tex}{tex}- ye^y +e^y=1{/tex}
0Thank You