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Find the equation of a curve whoise grad...

Find the equation of a curve whoise gradient is `(dy)/(dx)=(y)/(x)-"cos"^(2)(y)/(x)`, where `x gt 0, y gt 0` and which passes through the point `(1, (pi)/(4))` .

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The correct Answer is:
`tan((y)/(x))=1-log|x|`
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VIKRAM PUBLICATION ( ANDHRA PUBLICATION)-DIFFERENTIAL EQUATIONS -EXERCISE- 8(c)
  1. Solve the following differential equations. (dy)/(dx)=(x-y)/(x+y)

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  2. Solve the following differential equations. (x^(2)+y^(2))dy=2xy dx

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  3. Solve the following differential equations. (dy)/(dx)=(-(x^(2)+3y^(2)...

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  4. Solve the following differential equations. y^(2)dx+(x^(2)-xy)dy=0

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  5. Solve the following differential equations. (dy)/(dx)=((x+y)^(2))/(2x...

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  6. Solve the following differential equations. (x^(2)-y^(2))dx-xy dy=0

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  7. Solve the following differential equations. (x^(2)y-2xy^(2))dx=(x^(3)...

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  8. Solve the following differential equations. y^(2)dx+(x^(2)-xy+y^(2))d...

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  9. Solve the following differential equations. (y^(2)-2xy)dx+(2xy-x^(2))...

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  10. Solve the following differential equations. (dy)/(dx)+(y)/(x)=(y^(2))...

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  11. Solve the following differential equations. x dy-y dx= sqrt(x^(2)+y^(...

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  12. Solve the following differential equations. (2x-y)dy=(2y-x) dx

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  13. Solve the following differential equations. (x^(2)-y^(2))(dy)/(dx)=xy

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  14. Solve the following differential equations. 2(dy)/(dx)=(y)/(x)+(y^(2)...

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  15. Solve (1+e^((x)/(y)))dx+e^((x)/(y)) (1-(x)/(y))dy=0

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  16. Solve : x " sin"(y)/(x).(dy)/(dx)=y " sin"(y)/(x)-x

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  17. Solve : x dy= (y+x " cos"^(2)(y)/(x))dx

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  18. Solve : (x-y log y+y log x)dx+x(logy-logx)dy=0

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  19. Solve : (y dx+x dy)x "cos"(y)/(x)=(x dy-y dx) y " sin "(y)/(x)

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  20. Find the equation of a curve whoise gradient is (dy)/(dx)=(y)/(x)-"cos...

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