What is the solution for (dy)/(dx)+2y=e^{3x}y^2 ?

The solution for (dy)/(dx)+2y=e^{3x}y^2 is y= 1/(e^{2x)(-e^x+c_{1})}

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(dy)/(dx)+2y=e^{3x}y^2

\frac{d y}{d x} + 2 y = e^{3 x} y^{2}

y = \frac{1}{e ^{2 x} ( - e ^{x} + c _{1} )}

Solution steps

\frac{d y}{d x} + 2 y = e^{3 x} y^{2}

Solve Bernoulli ODE:

y = \frac{1}{e ^{2 x} ( - e ^{x} + c _{1} )}

y = \frac{1}{e ^{2 x} ( - e ^{x} + c _{1} )}

\int \frac{1}{1 + 1 - x ^{2}} d x

\int \frac{1}{( x ^{2} + 1 ) ^{3}} d x

\int sec^{2} (x) (1 + tan (x)) d x

\int \frac{1}{x + 1 - x ^{2}} d x

What is the solution for (dy)/(dx)+2y=e^{3x}y^2 ?
The solution for (dy)/(dx)+2y=e^{3x}y^2 is y= 1/(e^{2x)(-e^x+c_{1})}