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Verify that the given fuction (implicit or explicit) is a solution of the corresponding differential equation.
`xy = a e^x + be^-x + x^2 :x (d^2y)/(dx^2)+2dy/dx -x y + x^2 - 2 = 0`

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

Verify that the given fuction (implicit or explicit) is a solution of the corresponding differential equation. y = x sin 3x : (d^2y)/(dx^2) + 9y - 6 cos 3x = 0

Verify that the given function (explicit or implicit) is a solution of the correseponding differential equation : y = Ax : xy' = y( x ne 0)

Verify that the given function (explicit or implicit) isa solution of the correseponding differential equation : y = e^x + 1 : y'' - y' = 0

Verify that the given fuction (implicit or explicit) is a solution of the corresponding differential equation. x^2 = 2y^2 log y : (x^2 + y^2) (dy)/(dx) - xy = 0

Verify that the given function (explicit or implicit) isa solution of the correseponding differential equation : y = cos x + c : y' + sin x = 0

Verify that the given function (explicit or implicit) isa solution of the correseponding differential equation : y = x^2 + 2x +c :y' - 2x - 2 = 0

Verify that the given function (explicit or implicit) isa solution of the correseponding differential equation : y = sqrt(1 + x^2) : y' = (xy)/(1 + x^2)

Verify that the given function (explicit or implicit) is a solution of the correseponding differential equation : x + y = tan^-1 y : y^2 y' + y^2 + 1 = 0

Verify that the given functions (explicit or implicit) is the solution of the corresponding differential equation . (x+y)=tan ^-1 y , y^2 y^'+y^2+1=0

V PUBLICATION-DIFFERENTIAL EQUATIONS-QUESTION BANK
  1. Solve the differential equation (tan ^-1 y-x) d y=(1+y^2) d x

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  2. For each of the differential equations given below, indicate its order...

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  3. Verify that the given fuction (implicit or explicit) is a solution of ...

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  4. Form the differential equation representing the family of curves given...

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

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  6. Form the differential equation of the family of circles in the first q...

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  7. Find the general solution of the differential equation. (dy)/(dx)+sqrt...

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  8. Show that the general solution of the differential equation (dy)/(dx)+...

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

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

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  11. Solve the differential equation y e^(x/y) d x=(x e^(x/y)+y^2) d y(y ne...

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  12. Find a particular solution of the differential equation (x-y)(d x+d y)...

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  13. Solve the differential equation [(e^(-2 sqrtx)/sqrtx)-(y/(sqrtx))] ((...

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

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  15. Find the general solution of the differential equation (x+1)(dy)/(dx) ...

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  16. The population of a village increases continuously at the rate. propor...

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  17. The general solution of the differential equation (y dx - x dy)/y=0.

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  18. Choose the correct answer. The general solution of a differential equa...

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  19. Choose the correct answer. The general solution of a differential equa...

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  20. Form the differential equation corresponding to y=a x^2+b x+c

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