Solve the Bernoulli equation dydt y ty3Solutiondyy3 1y2 dt

Solve the Bernoulli equation dy/dt - y = ty3

Solution

dy/y³ -1/y² dt= t dt

put 1/y² = m

-2/y³ dy   =   dm

-dm/2 - m dt = t dt

multiply both sides by integrating factor: e^2t

e^2t dm + 2m e^2t dt = -2 t e^2t dt

left side perffect integral :

m e^2t = -2 [ t e^2t /2 - e^2t /4 ] + c

(1/y²) = -t   + (1/2) + c e^-2t

1 = -t y² + y² /2 + c y² e^-2t answer !!!