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Prove that xy= ae^(x)+be^(-x)+x^(2) is t...

Prove that `xy= ae^(x)+be^(-x)+x^(2)` is the general solution of the differential equation `x(d^(2)y)/(dx^2)+2(dy)/(dx)-xy+x^(2)-2=0`

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ARIHANT PUBLICATION-DIFFERENTIAL EQUATION-CHAPTER PRACTICE (VERY SHORT ANSWER TYPE QUESTIONS)
  1. Show that the function y=(A+Bx)e^(3x) is a solution of the equation (d...

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  2. Show that y= Cx+(a)/(C ) is a solution of differential equation y= x(d...

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  3. Prove that xy= ae^(x)+be^(-x)+x^(2) is the general solution of the dif...

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  4. Show that the function phi, defined by phi(x)= cos x(x in R), satisfie...

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  5. Find the differential equation of the family of all straight lines.

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  6. Write the differential equation of all non-horizontal lines in a plane...

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  7. Write the differential equation representing the family of curves y= m...

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  8. Find the differential equation of the family of concentric circles hav...

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  9. Find the differential equation of the family of curves y= Ae^(x)+Be^(-...

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  10. Form the differential equation by aliminating A and B in Ax^(2)+By^(2)...

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  11. Find the differential equation corresponding to curve y= a cos (x+b), ...

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  12. Solve the following differential equations : (dy)/(dx)= sqrt(1-y^2),...

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  13. Solve the following differential equations : (dy)/(dx)+y=1, y ne 1.

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  14. Solve the following differential equations : (dy)/(dx)-(y(x+1))/(x)=...

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  15. Solve the following differential equations : (dy)/(dx)=e^(x+y)+x^(2)...

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  16. Write the solution of differential equation (e^(x)+e^(-x))dy= (e^(x)-e...

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  17. If (dy)/(dx)=ye^(x)" and "x=0, y= e, then find the value of y, when x=...

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  18. Solve 2(y+3)-xy(dy)/(dx)=0, given that y(1)= -2.

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  19. Solve the differential equation (dy)/(dx)= y sin 2x, given that y(0)= ...

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  20. Solve the initial value problem dy= e^(2x+y)dx, y(0)= 0.

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