What is the solution for (dy)/(dx)=(4x^2+3x+2)(y+5) ?

The solution for (dy)/(dx)=(4x^2+3x+2)(y+5) is y=e^{(4x^3)/3+(3x^2)/2+2x+c_{1}}-5

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(dy)/(dx)=(4x^2+3x+2)(y+5)

\frac{d y}{d x} = (4 x^{2} + 3 x + 2) (y + 5)

y = e^{\frac{4 x ^{3}}{3} + \frac{3 x ^{2}}{2} + 2 x + c_{1}} - 5

Solution steps

\frac{d y}{d x} = (4 x^{2} + 3 x + 2) (y + 5)

Solve separable ODE:

y = e^{\frac{4 x ^{3}}{3} + \frac{3 x ^{2}}{2} + 2 x + c_{1}} - 5

y = e^{\frac{4 x ^{3}}{3} + \frac{3 x ^{2}}{2} + 2 x + c_{1}} - 5

\int 1.5 x d x

(x^{2} + 4), (- x^{2} - 1), x = - 2, x = 3

t \to 2 lim (6 t^{2} - 3 t + 1)

\frac{- s - 4}{s ^{2} + 4 s + 3}

\int 1 + y^{3} d y

What is the solution for (dy)/(dx)=(4x^2+3x+2)(y+5) ?
The solution for (dy)/(dx)=(4x^2+3x+2)(y+5) is y=e^{(4x^3)/3+(3x^2)/2+2x+c_{1}}-5