यदि ` y= 3 e^(2x) + 2 e^(3x) ` है तो सिद्ध कीजिए कि =` (d^(2) y)/(dx^(2))- 5 (dy)/(dx) + 6y = 0 `

Explanation

` :' y = 3 e^(2x) + 2 e^(3x)`
` (dy)/(dx) = 3 d/(dx) e^(2x) + 2 d/(dx) e^(3x) `
` :. dy/dx 1 /sqrt(1 - x^(2))`
पुनः अवकलन करने पर,
` (d^(2)y) /(dx) = ((1=x^(2))1/2* d/dx (1) - 1 d/(dx) (1-x^(2)) ^(1/2))/(1-x^(2))`
या ` (1-x^(2)) (d^(2)y)/(dx^(2)) = (1-x^(2))^(1/2) xx 0 - 1 xx 1/2 ( 1-x^(2)) ^(1/2) xx (-2x) `
या ` (1-x^(2)) (d^(2)y)/(dx^(2)) = x/sqrt(1-x)^(2) `
या ` ( 1-x^(2)) (d^(2)y)/(dx^(2)) = x xx (dy)/(dx) `
` (1-x^(2)) (d^(2)y)/(dx^(2) - x) (dy)/(dx) = 0 `