What is the solution for (dy)/(dx)=3(1+y)(1-x) ?

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

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(dy)/(dx)=3(1+y)(1-x)

\frac{d y}{d x} = 3 (1 + y) (1 - x)

y = e^{3 (- \frac{x ^{2}}{2} + x) + c_{1}} - 1

Solution steps

\frac{d y}{d x} = 3 (1 + y) (1 - x)

Solve separable ODE:

y = e^{3 (- \frac{x ^{2}}{2} + x) + c_{1}} - 1

y = e^{3 (- \frac{x ^{2}}{2} + x) + c_{1}} - 1

\int \frac{1}{x 36 x ^{2} - 36} d x

\int \frac{x}{x + 15} d x

\int \frac{x + sin ( x )}{1 + cos ( x )} d x

2 y^{^{''}} + 5 y^{^{'}} - 3 y = 0, y (0) = - 7, y^{^{'}} (0) = 28

(2 e^{2 x})^{^{'}}

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