Question

Solve equation and please state if; no solutions were lost, the solution x = 0 was lost or the solution y=0 was lost. Thank you

Solve the equation. (2x)dx + (y - 3x²y = 1)dy = 0 by multiplying by the integrating factor. An implicit solution in the form F(x,y) = C is = C, where C is an arbitrary constant, and (Type an expression using x and y as the variables.) no solutions were lost the solution x=0 was lost the solution y=0 was lost

Answer 1

♡ (2x) dx + (y-3x²4-1) dy N2X, May) Now , My - Nx 3 € for of y' only) N also IF- ro , y to o + 6xyt -M 2x B z dy -3 dogy e y 3 Multiplying the D.E by I-F= y3 we get (e) dx y - 3x²yt M y to + I dy (exact D.ES 3 N ,

then soln of (2) is given by SM, (x,y) dal = 6 + SN, (x,y) dy free- from a y Constant 21 22 dx + Siy-gdy = g-const + y2 С X² 23 y to =) 2 Hence, y=0 noth clost by multiply I. F-g3