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Show that y =a cos (log x)+b sin (logx),...

Show that y =a cos (log x)+b sin (logx),x`le`0 is a soluton of the differential equation `x^(2)y''+xy'+y=0`

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a cos (log x)+b sin (log x) is a solution of the given diffential equation
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FULL MARKS-ORDINARY DIFFERENTIAL EQUATIONS -ADDITIONAL PROBLEMS
  1. Show that y =a cos (log x)+b sin (logx),xle0 is a soluton of the dif...

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  2. Find the order and degree of the following differential equations ...

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  3. Find the differential equation of the family of straight lines y =m...

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  4. Find the differential equation that will represented family of all cir...

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  5. Form the differential equation from y^(2) = 4a (x-a)

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  6. Verify that the function y=a cos x + b sin x is a solution of the ...

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  7. Verify that the function y =4 sin 3x is a solution of the differentia...

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  8. Verify that function y=ax^(2)+bx+c is a solution of the differenti...

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  9. Verify that the function y=e^(-3x) is solution of the differential eq...

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  10. Solve e^(x)sqrt(1-y^(2))dx+(y)/(x)dy=0

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  11. Solve (x+y)^(2)(dy)/(dx) =a^(2)

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  12. Find the cubic polynomial in x which attains its maximum value 4 and m...

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  13. The normal lines to a given curve at each point (x,y) on the curve ...

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  14. Solve (2sqrt(xy-x)dy+dx=0

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  15. Solve (x^(3)+3xy^(2))dx+3x^(2)y)dy=0

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  16. Solve (dy)/(dx)=(y(x-2y))/(x(x-3y))

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  17. Solve (x^(2)+y^(2))dy=xydx

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  18. Find the equation of the curve passing through (1,0) and which has sl...

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  19. (dy)/(dx) + ycotx = 2cos x

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  20. Solve (1-x)^(2))(dy)/(dx)+2xy=xsqrt(1-x^(2))

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  21. Solve (x+1)(dy)/(dx)-y=e^(x)(x+1)^(2)

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