Question 366 of 490MediumMCQ
The general solution of the differential equation (y2
-- x3)dx -- xydy = 0 (x \[ \ne \] 0) is :
(where c is a constant of integration)
Solutions · 1
Official solution
(y2−x3)dx−xydy=0
\[ \Rightarrow y(ydx - xdy) = {x^3}dx\]
\[ \Rightarrow {y \over x}\left( {{{ydx - xdy} \over {{x^2}}}} \right) = dx\]
\[ \Rightarrow - {y \over x}d\left( {{y \over x}} \right) = dx\]
\[ \Rightarrow - {1 \over 2}{\left( {{y \over x}} \right)^2} = x + k\]
\[ \Rightarrow - {y^2} = 2{x^3} + 2{x^2}k\]
\[ \Rightarrow {y^2} + 2{x^3} + c{x^2} = 0\] Answer the question to unlock