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If y=e^m\ sin^((-1)x) , prove that (1-x^...

If `y=e^m\ sin^((-1)x)` , prove that `(1-x^2)(d^2y)/(dx^2)-x(dy)/(dx)-m^2y=0` .

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CBSE COMPLEMENTARY MATERIAL-DIFFERENTIAL EQUATIONS-FOUR MARK QUESTIONS
  1. If y=e^m\ sin^((-1)x) , prove that (1-x^2)(d^2y)/(dx^2)-x(dy)/(dx)-m^2...

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  2. Show that y=sin (sin x) is a solution of differential equation (d^2y)/...

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  3. Show that y=A x+B/x ,x!=0 is a solution of the differential equation x...

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  4. If y=Acos(logx)+\ Bsin(logx) , prove that x^2\ (d^2y)/(dx^2)+x(dy)/(dx...

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  5. Verify that y=log(x+^sqrt(x^2+a^2))^2 satisfies the differential eq...

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  6. The differential equation of the family of curves y=e^x(Acosx+Bsinx), ...

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  7. Find the differential equation of an ellipse with major and minor axes...

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  8. Form the differential equation representing the family of curves (y-b)...

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  9. Solve the following differential equations (1-x^2)(dy)/(dx)-xy=x^2" ...

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  10. Solve the following differential equations x(dy)/(dx)+2y= x^2 log x.

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  11. Solve the following differential equations (dy)/(dx)+(1)/(x)y = cos ...

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  12. Solve the differential equation "dy=cos x(2-y cosec x)dx" given that y...

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  13. Solve the following differential equations ydx+(x-y^3)dy=0.

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  14. Solve the following differential equations ye^(y)dx= (y^3+2xe^(y))dy...

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  15. Solve each of the following differential equations y-x(dy)/(dx)=2(y^...

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  16. Solve each of the following differential equations cos y "" dx +(1+2...

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  17. Solve the following differential equation: x\ sqrt(1-y^2)dx+y\ sqrt(1-...

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  18. Solve each of the following differential equations sqrt((1-x^2)(1-y^...

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  19. Solve each of the following differential equations (xy^2+x)dx+(yx^2+...

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  20. Solve each of the following differential equations (dy)/(dx)-y sin^3...

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