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Solve the differential equation (dy)/(dx...

Solve the differential equation `(dy)/(dx)=(x(2logx+1))/((siny+ycosy))`.

A

`ysiny=x^(2)logx+x^(2)/2+c`

B

`ycosy=x^(2)(logx+1)+c`

C

`ycosy=x^(2)logx+x^(2)/2+c`

D

`ysiny=x^(2)logx+c`

Text Solution

Verified by Experts

The correct Answer is:
D
`(ycosy+siny)dy=(2xlogx+x)dx`
`ysiny-intsinydy+int(sinydx)`
`=x^(2)logx-intx^(2)1/xdx+intxdx+c`
`therefore ysiny=y^(2)logx+c`
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CENGAGE-DIFFERENTIAL EQUATIONS-Exercise (Single)
  1. If y=y(x) and ((2+sinx)/(y+1))dy/dx=-cosx, y(0)=1, then y(pi/2) equa...

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  2. The equation of the curves through the point (1, 0) and whose slope...

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  3. Solve the differential equation (dy)/(dx)=(x(2logx+1))/((siny+ycosy)).

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  4. The solution of the equation (x^2y+x^2)dx+y^2(x-1)dy=0 is given by (a)...

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  5. Solve the following differential equations (dy)/(dx)=sinx*siny

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  6. The solution of (d v)/(dt)+k/m v=-g is (a) ( b ) (c) v=c (d) e^(( e...

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  7. The general solution of the differential equation (dy)/(dx)+sin(x+y)/2...

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

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

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

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

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

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

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  14. The solution of the differential equation y^(')y^(''')=3(y^(''))^(2) i...

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  15. The solution of the differential equation y^-8y^=0, where y(0)=1/8,y^(...

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

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

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

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

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  20. The solution of (y+x+5)dy=(y-x+1)dx is (a) ( b ) (c)log(( d ) (e) (f)...

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