solve-y-1-4x-2-8y-0-

Question Number 38802 by tawa tawa last updated on 30/Jun/18

solve : y^{″} (1 + {4 x}^{2}) - 8 y = 0

Answered by MrW3 last updated on 30/Jun/18

y = {a x}^{2} + b x + c

y^{'} = 2 a x + b

y^{″} = 2 a

2 a (1 + 4 x^{2}) - 8 ({a x}^{2} + b x + c) = 0

8 {a x}^{2} + 2 a - 8 {a x}^{2} - 8 b x - 8 c = 0

- 8 b x + 2 a - 8 c = 0

\Rightarrow - 8 b = 0 \Rightarrow b = 0

\Rightarrow 2 a - 8 c = 0 \Rightarrow a = 4 c

\Rightarrow y = c (4 x^{2} + 1)

Commented by tawa tawa last updated on 30/Jun/18

God bless you sir .

Answered by tanmay.chaudhury50@gmail.com last updated on 30/Jun/18

y = x^{α} + h b y t r i a l m e t h o d

y = x^{2} + \frac{1}{4} i s a s o l u t i o n \dots

\frac{d y}{d x} = 2 x \frac{d^{2} y}{{d x}^{2}} = 2

2 (1 + 4 x^{2}) - 8 (x^{2} + \frac{1}{4}) = 0

\boldsymbol S O y = x^{2} + \frac{1}{4} i s t h e s o l u t i o n

p l s g i v e m e t i m e t o s o l v e b y s t a n d a r d m e t h o d

Commented by tawa tawa last updated on 30/Jun/18

i will be waiting sir . God bless you

i will be waiting sir . God bless you