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Find the solution of differential equati...

Find the solution of differential equation `x^(2)=1 + (x/y)^(-1) (dy)/(dx) + ((x/y)^(-2)((dy)/(dx))^(2))/(2!)+.....`

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`x^(2)=e^((x/y)^(-1)(dy)/(dx))=e^((y/x)(dy)/(dx))`
or `"ln "x^(2)=y/x(dy)/(dx)`
or `intx" ln "x^(2)dx=intydy`
Putting `x^(2)=t`, we get `2xdx=dt`
or `1/2 int " ln" t dt =y^(2)/2`
or `c+t" ln "t-t=y^(2)`
or `y^(2)=x^(2)" ln "x^(2)-x^(2)`
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CENGAGE-DIFFERENTIAL EQUATIONS-Exercise (Single)
  1. The general solution of the differential equation (dy)/(dx)+sin(x+y)/2...

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  2. if y+x(dy)/(dx)=x(phi(xy))/(phi'(xy)) then phi(xy) is

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  3. Find the solution of differential equation x^(2)=1 + (x/y)^(-1) (dy)/(...

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  4. The solution of the differential equation (x+(x^3)/(3!)+(x^5)/(5!)+)/...

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  5. The solution of the differential equation x=1+x y(dy)/(dx)+(x^2y^2)/(...

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  6. A curve passing through (2,3) and satisfying the differential equat...

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  7. The solution of the differential equation (d^2y)/(dx^2)=sin3x+e^x+x^2 ...

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  8. Find the solution of the differential equation y^(')y^(''')=3(y^(''))^...

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  9. The solution of the differential equation y^(prime prime prime)-8y^(pr...

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  10. The slope of the tangent at (x , y) to a curve passing through (1,p...

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  11. Solve x((dy)/(dx))=y(logy-logx+1)

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  12. The solution of differential equation x y^(prime)=x((y^2)/(x^2)+(f((y^...

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  13. The solution of (x^2+x y)dy=(x^2+y^2)dx is (a) ( b ) (c)logx=log(( d ...

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  14. The solution of (y+x+5)dy=(y-x+1)dx is

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  15. The slope of the tangent at (x , y) to a curve passing through a po...

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  16. Solution of the differential equation ydx-xdy+xsqrt(xy)dy=0 is

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  17. The solution of (x^2dy)/(dx)-x y=1+cosy/x is (a) ( b ) (c)tan(( d ) (...

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  18. The solution of the differential equation 2x^2y(dy)/(dx)=tan(x^2y^2)-2...

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  19. Solution of the differential equation {1/x-(y^2)/((x-y)^2)}dx+{(x^2)/(...

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  20. The solution of differential equation (2y+x y^3)dx+(x+x^2y^2)dy=0 is (...

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