Solve the differential equation $y dy/dx-y^2+9x=0$ ?

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Answer 1 · 2017-03-21T12:44:35

$y = sqrt( C_0 e^(2x)+9(x+1/2))$

Think that

$y(dy)/(dx) = 1/2 d/(dx) y^2$ so the equation can be read as

$1/2 d/(dx) y^2-y^2+9x=0$ now calling $z=y^2$ we have

$1/2 (dz)/(dx)-z+9x=0$ . This equation is easy to solve giving

$z = C_0 e^(2x)+9(x+1/2)$ and finally

$y = sqrt z = sqrt( C_0 e^(2x)+9(x+1/2))$

Solve the differential equation y dy/dx-y^2+9x=0y dy/dx-y^2+9x=0 ?