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Solve the equation (dy)/(dx)=y/(2y1ny+y-...

Solve the equation `(dy)/(dx)=y/(2y1ny+y-x)`

Text Solution

Verified by Experts

The correct Answer is:
`xy=y^(2)log_(e)y+c`
Given equation is `(dy)/(dx) = (2y " ln " y+y-x)/(y)`
or `(dx)/(dy)+1/yy=(2"ln "y+1)`
I.F. =y and solution is `xy=int(2" ln "+1)ydy+c`
or `xy=y^(2) " ln "y+c`
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CENGAGE PUBLICATION-DIFFERENTIAL EQUATIONS-All Questions
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  2. Solve the equation (1-x^2)((dy)/(dx))+2x y=xsqrt(1-x^2)

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  3. Solve the equation (dy)/(dx)=y/(2y1ny+y-x)

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  4. Solve the equation ydx+(x-y^2)dy=0

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  5. Find the equation of a curve passing through (0,1) and having gradient...

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  6. Solve the equation (dy)/(dx)=1/x=(e^y)/(x^2)

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  7. (dy)/(dx)+xsin2y=x^(3)cos^(2)y

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  8. (dy)/(dx) + (xy)/(1-x^(2))=xsqrt(y)

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  9. (dy)/(dx)=(x^(3)-2xtan^(-1)y)(1+y^(2))

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  10. (dy)/(dx)=(tanx)/(1+x)e^(x) secy

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  11. Find the equation of the curve in which the subnormal varies as the ...

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  15. A normal is drawn at a point P(x , y) of a curve. It meets the x-ax...

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  16. Find the orthogonal trajectories of family of curves x^2+y^2=c x

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  17. A curve C has the property that if the tangent drawn at any point P...

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  18. A person places Rs 500 in an account that interest compounded continuo...

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  20. If the population of country double in 50 years, in how many years wil...

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