What is the solution for x^4e^y+(x+1)y(dy)/(dx)=0 ?

The solution for x^4e^y+(x+1)y(dy)/(dx)=0 is y=-\W((-3x^4+4x^3-6x^2+12x-12ln(x+1)+c_{1})/(12e))-1

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x^4e^y+(x+1)y(dy)/(dx)=0

x^{4} e^{y} + (x + 1) y \frac{d y}{d x} = 0

y = - W (\frac{- 3 x ^{4} + 4 x ^{3} - 6 x ^{2} + 12 x - 12 ln ( x + 1 ) + c _{1}}{12 e}) - 1

Solution steps

x^{4} e^{y} + (x + 1) y \frac{d y}{d x} = 0

Solve separable ODE:

y = - W (\frac{- 3 x ^{4} + 4 x ^{3} - 6 x ^{2} + 12 x - 12 ln ( x + 1 ) + c _{1}}{12 e}) - 1

y = - W (\frac{- 3 x ^{4} + 4 x ^{3} - 6 x ^{2} + 12 x - 12 ln ( x + 1 ) + c _{1}}{12 e}) - 1

f (x) = (1 + cos^{2} (x))^{6}

arcsin (x)

\int_{5}^{10} a x - 10 b d x

f (x) = \frac{12}{x}, at x = - 2

\frac{d}{d z} (0)

What is the solution for x^4e^y+(x+1)y(dy)/(dx)=0 ?
The solution for x^4e^y+(x+1)y(dy)/(dx)=0 is y=-\W((-3x^4+4x^3-6x^2+12x-12ln(x+1)+c_{1})/(12e))-1