If y = y x satisfies the differential equation 8 x 9 + x d y = 4 + 9 + x - 1 d x and x > 0 ,   y 0 = 7 , then y 256 =

Question

If y = y x satisfies the differential equation 8 x 9 + x d y = 4 + 9 + x - 1 d x and x &#62; 0 , &#160; y 0 = 7 , then y 256 =

Aicharya · Accepted Answer

y = 1 8 &#160; &#8747; d x 4 + 9 + x &#160; . &#160; x &#160; . &#160; 9 + x Put 9 + x = t &#160; &#160; &#160; &#160; &#8658; d x x &#160; . &#160; 9 + x = 4 d t &#8756; &#160; y = 4 8 &#160; &#8747; d t 4 + t &#8658; y = &#160; 4 + t + C &#8658; y x = &#160; 4 + 9 + x + C At x = 0 : y 0 = &#160; 7 &#160; &#160; &#8658; &#160; &#160; &#160; C = 0 &#8756; &#160; y x = &#160; 4 + 9 + &#160; x &#8658; y 256 = 3

If y = y x satisfies the differential equation 8 x 9 + x d y = 4 + 9 + x - 1 d x and x > 0 ,   y 0…

Solution

If y = y x satisfies the differential equation 8 x 9 + x d y = 4 + 9 + x - 1 d x and x &#62; 0 , &#160; y 0…

Solution

If y = y x satisfies the differential equation 8 x 9 + x d y = 4 + 9 + x - 1 d x and x > 0 , y 0…