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Show that x y=a x^x+b e^(-x)=x^2 is a so...

Show that `x y=a x^x+b e^(-x)=x^2` is a solution of the differential equation. `x(d^2y)/(dx^2)+2-x y+x^2-2=0.`

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RD SHARMA ENGLISH-DIFFERENTIAL EQUATION-All Questions
  1. Form the differential equation of the family of hyperbolas having f...

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  2. Form the differential equation of the family of circles in the seco...

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  3. Show that x y=a x^x+b e^(-x)=x^2 is a solution of the differential equ...

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  4. Verify that the function y=C1e^(a x)cosb x+C2e^(ax)sinb x ,\ C1, C2,\ ...

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  5. Show that y=b e^x+c e^(2x)\ is a solution of the differential equatio...

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  6. Verify that y=4sin3x is a solution of the differential equation (d^2y)...

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  7. Show that y=a e^(2x)+b e^(-x) is a solution of the differential equati...

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  8. Show that the function y=A cos x+b sinx is as solution of the differe...

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  9. Show that the function y=A cos\ 2x-B sin\ 2x\ is a solution of the di...

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  10. Show that\ y=A e^(B x) is as solution of the differential equation (d^...

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  11. Verity that y=a/x+b is a solution of the differential equation (d^2y)/...

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  12. Verify that y^2=4a x is a solution of the differential equation y=x(dy...

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  13. Show that A x^2+B y^2=1 is a solution of the differential equation x{y...

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  14. Show that y=a x^3+b x^2+c is a solution of the differential equation (...

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  15. Show that y=(c-x)/(1+c x) is a solution of the different equation (1+x...

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  16. Show that y=e^x(A\ cos x+Bsinx) is the solution of the differential eq...

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  17. Verify thaty=c x+2c^2 is a solution of the differential equation 2((dy...

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  18. Verify that y=-x-1 is a solution of the differential equation (y...

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  19. Verity that y^2=4a\ (x+a) is a solution of the differential equatio...

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  20. Verify that y=e^(m cos^-1 x) satisfies the differential equation (1-x...

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