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if `a,b` are two positive numbers such that ` f(a+x)=b+[b^3+1-3b^2f(x)+3b{f(x)}^2-{f(x)}^3]^(1/3)` for all real `x`, then prove that `f(x)` is periodic and find its period?

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RD SHARMA ENGLISH-DIFFERENTIAL EQUATION-All Questions
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  2. Solve the initial value problem y^(prime)=ycot2x ,y(pi/4)=2.

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  3. if a,b are two positive numbers such that f(a+x)=b+[b^3+1-3b^2f(x)+3b...

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

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  5. Solve the initial value problem: x(xdy+ydx)=ydx ,y(1)=1.

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  6. Solve: (dy)/(dx)=ysin2x it being given that y(0)=1.

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  7. Solve the initial value problem: (xdy+ydx)=xy dx ,y(1)=1.

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  8. Find the equation of the curve passing through origin if the slope ...

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  9. Find the equation of the curve passing through the point (1,0) if t...

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  10. Find the equation of the curve passing through the point (-2,3) giv...

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  11. Find the equation of the curve passing through the point (1,1) whos...

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  12. Solve the following differential equation : xcosy\ dy=(x e^xlogx+e^x)...

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  13. Solve the following differential equations: xcos^2y \ dx=ycos^2x \ dy

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  14. Experiments show that the rate of inversion of cane sugar in dilute so...

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  15. In a culture, the bacteria count is 1,00,000. The number is increas...

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  16. A bank pays interest by continuous compounding, that is ,by treatin...

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  18. The equation of the curve passing through the point (1,pi/4) and havin...

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  19. Find the equation to the curve satisfying x(x+1)(dy)/(dx)-y=x(x+1) and...

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  20. The curve is such that the length of the perpendicular from the ori...

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