y-dy-dx-d-2-y-dx-2-d-3-y-dx-3-solve-this-diffrential-equation-

Question Number 142079 by rs4089 last updated on 26/May/21

y = \frac{d y}{d x} + \frac{d^{2} y}{{d x}^{2}} + \frac{d^{3} y}{{d x}^{3}} + \dots . .

s o l v e t h i s d i f f r e n t i a l e q u a t i o n

Answered by Dwaipayan Shikari last updated on 26/May/21

y = y^{'} + y^{″} + y^{^{‴}} + \dots y = {C e}^{λ x}

e^{λ x} = λ e^{λ x} + λ^{2} e^{λ x} + \dots

1 = λ + λ^{2} + λ^{3} + \dots \Rightarrow 1 = \frac{λ}{1 - λ} \Rightarrow λ = \frac{1}{2}

y = C \sqrt{e^{x}}

Answered by mindispower last updated on 26/May/21

y = y^{'} + y^{'} \Rightarrow y = 2 y^{'} \Rightarrow y = {k e}^{\frac{x}{2}}

Answered by mnjuly1970 last updated on 26/May/21

y^{'} = - y^{'} + y

y^{'} = \frac{y}{2} \dots . ≫ l n (y) = \frac{x}{2} + C

\dots \dots y = {k e}^{\frac{x}{2}} \dots . .