Thread: Solving Bernoulli Differential Equation.

Originally Posted by amro05

Start by making the substitution .

Originally Posted by prove it

start by making the substitution .

yes sir i did it

but the problem is the absulet number (( 2 )) << without it , it became easy

Originally Posted by amro05

Applying the 'standard procedure' the substitution leads to the DE...

(1)

... which is known as 'Riccati Equation'. The solution of this type of equation is usually an hard task but, may be, not impossible in this case. The question requires further investigation...

Kind regards

Originally Posted by chisigma

Applying the 'standard procedure' the substitution leads to the DE...

(1)

... which is known as 'Riccati Equation'. The solution of this type of equation is usually an hard task but, may be, not impossible in this case. The question requires further investigation...

Kind regards

thank you sir for your help

I begin with


and I start with y1=2 and with y1=2x >>> but both gives more complicate Eq.

thank you sir for your help

Originally Posted by amro05

The original DE...

(1)

... is itself a 'Riccati Equation' so that a substitution of the type is useless. More promising is the substiution after that the (1) becomes...

(2)

The (2) is also a 'Riccati Equation' but, very important detail, we can verify that is solution of (2) and that allows You to find the general solution as follows. Setting the (2) becomes...

(3)

... which is a 'Bernoulli Equation', the solution of which is left to You...

Kind regards

Originally Posted by chisigma

Kind regards

Thank you very very mach .
all the best