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Question Number 2070 by Rasheed Soomro last updated on 01/Nov/15
(d/dx)((d^2 y/dx^2 ))=(d^2 /dx^2 )((dy/dx))  y=?
$$\frac{{d}}{{dx}}\left(\frac{{d}^{\mathrm{2}} {y}}{{dx}^{\mathrm{2}} }\right)=\frac{{d}^{\mathrm{2}} }{{dx}^{\mathrm{2}} }\left(\frac{{dy}}{{dx}}\right) \\ $$$${y}=? \\ $$
Commented by 123456 last updated on 01/Nov/15
f∈C^3
$${f}\in\mathrm{C}^{\mathrm{3}} \\ $$
Answered by prakash jain last updated on 01/Nov/15
(d/dx)((d^2 y/dx^2 ))=(d^2 /dx^2 )((dy/dx))  LHS=RHS  In function which can be triple differentiated  will satisfy the equation.
$$\frac{{d}}{{dx}}\left(\frac{{d}^{\mathrm{2}} {y}}{{dx}^{\mathrm{2}} }\right)=\frac{{d}^{\mathrm{2}} }{{dx}^{\mathrm{2}} }\left(\frac{{dy}}{{dx}}\right) \\ $$$$\mathrm{LHS}=\mathrm{RHS} \\ $$$$\mathrm{In}\:\mathrm{function}\:\mathrm{which}\:\mathrm{can}\:\mathrm{be}\:\mathrm{triple}\:\mathrm{differentiated} \\ $$$$\mathrm{will}\:\mathrm{satisfy}\:\mathrm{the}\:\mathrm{equation}. \\ $$$$ \\ $$
Commented by Rasheed Soomro last updated on 01/Nov/15
Will  every function which can be triple differentiated    satisfy?
$${Will}\:\:{every}\:{function}\:{which}\:{can}\:{be}\:{triple}\:{differentiated} \\ $$$$\:\:{satisfy}? \\ $$
Commented by prakash jain last updated on 01/Nov/15
yes. LHS=(d/dx)((d/dx)((dy/dx)))=RHS
$${yes}.\:\mathrm{LHS}=\frac{{d}}{{dx}}\left(\frac{{d}}{{dx}}\left(\frac{{dy}}{{dx}}\right)\right)=\mathrm{RHS} \\ $$
Commented by Rasheed Soomro last updated on 02/Nov/15
This means it is like an identity.It is no longer  conditional equation.
$${This}\:{means}\:{it}\:{is}\:{like}\:{an}\:{identity}.{It}\:{is}\:{no}\:{longer} \\ $$$${conditional}\:{equation}. \\ $$

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