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For each of the exercises given below, ...

For each of the exercises given below, verify that the given function (implicit or explicit) is a solution of the corresponding differential equation.(i) `y=a e^x+b e^(-x)+x^2` : `x(d^2y)/(dx^2)+2y(dy)/(dx)-x y+x^2-2=0`(ii) `y=e^x(acosx+bsin

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MODERN PUBLICATION-DIFFERENTIAL EQUATIONS-Miscellaneous Exercise on Chapter 9
  1. Determine the order and degree of each of the following differentia...

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  2. Find the order and degree (if defined) of the equation: (d^4y)/(dx^4)...

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  3. For each of the exercises given below, verify that the given function...

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  4. The differential equation for y=e^(x)(acosx+bsinx) is

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  5. For each of the exercises given below, verify that the given function ...

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  6. if x^2=2y^2logy then prove (x^2+y^2)(dy)/(dx)-xy=0

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  7. Form the differential equation representing the family of curves give...

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  8. Prove that x^2-y^2=c(x^2+y^2)^2is the general solution of differenti...

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  9. Form the differential equation of the family of circles in the firs...

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

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  11. Show that the general solution of the differentia equation (dy)/(dx...

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  12. Find the equation of the curve passing through the point (0,pi/4) w...

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  13. Find the particular solution of the differential equation (1+e^(2x))dy...

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  14. Solve the differential equation : y e^(x//y)dx=(x e^(x//y)+y^(2))dy(...

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  15. Solve (x-y)(dx+dy)=dx-dy, given that y=-1, where x=0.

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  16. Solve [(e^(-2sqrt(x)))/(sqrt(x))-y/(sqrt(x))](dx)/(dy)=1(x!=0

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  17. Find the particular solution of the differential equation. (dy)/(dx...

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  18. Find a particular solution of the differential equation (x+1)(dy)/(dx...

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  19. The population of a village increases continuously at the rate proport...

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  20. The general solution of the differential equation (ydx-xdy)/(y)=0 is :

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