Dear experts in differential equations if there are 3 arbitary constants then is it necessary that we should differentiate thrice - Maths - Differential Equations

Question

Dear experts in differential equations if there are 3 arbitary
constants then is it necessary that we should differentiate thrice?
In case we are able to obtain an equation eliminating all the
constants by differentiating twice,is it right?

Aarushi Mishra · Accepted Answer

If you have 3 arbitary constants then you need to differentiate thrice, because you need 3 equations to find value of three arbitary constant, then your main equation will give relation between these three and you will put their values and get a differential equation
However if you are getting differentiaal equation by differentiating twice only then it is because 2 variables can be combined into one in that equationE
g
 y=cex+kOne notice two arbitary costant but actuallyy=cex+k=y=cy=cekex=k'ex, where k'=cek, thus here you need to differentiate once only

Dear experts in differential equations if there are 3 arbitary constants then is it necessary that we should differentiate thrice? In case we are able to obtain an equation eliminating all the constants by differentiating twice,is it right?