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Verify that the function y=c1 e^(a x) co...

Verify that the function `y=c_1 e^(a x) cos b x+c_2 e^(a x) sin b x`, where `c_1, c_2` are arbitrary constants is a solution of the differential equation.
`((d^2 y)/(d x^2))-2 a (dy)/(dx)+(a^2+b^2) y=0`

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V PUBLICATION-DIFFERENTIAL EQUATIONS-QUESTION BANK
  1. The Integrating Factor of the differential equation x (dy)/(dx)-y=2 x^...

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  2. The intergrating factor of the differential equation (1 -y^2)(dx)/(dy...

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  3. Verify that the function y=c1 e^(a x) cos b x+c2 e^(a x) sin b x, wher...

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  4. Form the differential equation of the family of circles in the second ...

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  5. Find the particular solution of the differential equation log ((dy)/(d...

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  6. Solve the differential equation (x d y-y d x) y sin (y/x)=(y d x+x d y...

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  7. Solve the differential equation (tan ^-1 y-x) d y=(1+y^2) d x

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

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

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

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

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

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

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

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

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

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

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

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

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

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