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