If-x-2-y-2-a-2-find-d-2-y-dx-2-if-a-is-constant-

Question Number 54880 by Otchere Abdullai last updated on 14/Feb/19

I f x^{2} - y^{2} = a^{2} f i n d \frac{d^{2} y}{{d x}^{2}} i f a i s

c o n s t a n t .

Answered by kaivan.ahmadi last updated on 14/Feb/19

f (x, y) = x^{2} - y^{2} - a^{2} = 0

y_{x}^{^{'}} = \frac{dy}{dx} = - \frac{f_{x}}{f_{y}} = - \frac{2 x}{- 2 y} = \frac{x}{y}

\frac{d^{2} y}{{dx}^{2}} = \frac{1 \times y - y_{x}^{^{'}} \times x}{y^{2}} = \frac{y - \frac{x^{2}}{y}}{y^{2}} = \frac{y^{2} - x^{2}}{y^{3}}

Commented by Otchere Abdullai last updated on 14/Feb/19

T h a n k s s i r!

Answered by tanmay.chaudhury50@gmail.com last updated on 14/Feb/19

y^{2} = x^{2} - a^{2}

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

y \times \frac{d^{2} y}{{d x}^{2}} + {(\frac{d y}{d x})}^{2} = 1

y (\frac{d^{2} y}{{d x}^{2}}) = 1 - {(\frac{x}{y})}^{2}

\frac{d^{2} y}{{d x}^{2}} = \frac{y^{2} - x^{2}}{y^{3}} \to \frac{d^{2} y}{{d x}^{2}} = \frac{- a^{2}}{y^{3}}

\frac{d^{2} y}{{d x}^{2}} = \frac{- a^{2}}{{(x^{2} - a^{2})}^{\frac{3}{2}}}

Commented by Otchere Abdullai last updated on 14/Feb/19

T h a n k s p r o f

Commented by tanmay.chaudhury50@gmail.com last updated on 14/Feb/19

i a m n o t a p r o f e s s o r b u t 49 y e a r s o l d i n d i a n i n t e r e s t d

i n m a t h e m a t i c s p h y s i c s a n d m y t h o l o g y, m e t a p h y s i c s

u n s o l v e d m y s t r y \dots

Commented by Otchere Abdullai last updated on 14/Feb/19

y e s i g a v e y o u t h e p r o f e s s o r b e c a u s e

y o u h a v e d o n e g r e a t c o n t r i b u t i o n t o

t h e g r o u p

Commented by $@ty@m last updated on 14/Feb/19

Y e a h .

H e d e s e r e v e s t h e t i t l e o f “ H o n o r a r y {P r o f e s s o r}^{″} .

Commented by Otchere Abdullai last updated on 14/Feb/19

Y e s y o u a r e r i g h t {d o n}^{'} t f o r g e t M r W

w a s t h e f i r s t h o n o u r e d p r o f e s s o r

s o i a l w a y s u s e p r o f W i n s t e r e d o f M r .

Commented by rahul 19 last updated on 14/Feb/19

N o t o n l y h i m, b u t M r W s i r, M j s s i r,

A j f o u r s i r t o o o o!