Question

x dy/dx-y=sinx〖.y〗^2

Answer 1

divide x through out, its a bernouli equation too

familiar with solving these ?

Answer 2

\[\rm x\dfrac{dy}{dx} - y = (\sin x )(y^2)\]

like this ?

Answer 3

dividign `xy^2` through out, you get :
\[\rm \frac{1}{y^2}\dfrac{dy}{dx} -\frac{1}{x}\frac{1}{y} = \frac{\sin x}{x} \]

Answer 4

substitute \(\large \rm \frac{1}{y} = v \implies \frac{1}{y^2}\frac{dy}{dx} = -\frac{dv}{dx}\)

Answer 5

the equation becomes :
\[\rm -\frac{dv}{dx} - \dfrac{1}{x}v = \dfrac{\sin x}{x}\]

Answer 6

which is same as :

\[\rm \frac{dv}{dx} + \dfrac{1}{x}v = -\dfrac{\sin x}{x}\]

Answer 7

its a linear equation now, find the integrating factor and see if u can take it home

Answer 8

k i got it
thanq very much

Answer 9

yw:)