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Popular >

e^yy^'=(x+e^y-1)

Solution

e^{y} y^{^{'}} = (x + e^{y} - 1)

Solution

y = ln (c_{1} - e^{- x} x) + x

Solution steps

e^{y} y^{'} (x) = (x + e^{y} - 1)

Solve exact ODE:

y = ln (c_{1} - e^{- x} x) + x

y = ln (c_{1} - e^{- x} x) + x

Popular Examples

integral of x^2sqrt(7x+8)

\int x^{2} 7 x + 8 d x

simplify d/(dd)(ax^3+bx^2+cx+d)simplify

\frac{d}{dd} (a x^{3} + b x^{2} + c x + d)

integral of 2/3 e^{3x}

\int \frac{2}{3} e^{3 x} d x

derivative of (x^3-2x(-x+6x^2))

\frac{d}{d x} ((x^{3} - 2 x) (- x + 6 x^{2}))

(e^{2x}+9)(dy)/(dx)=y

(e^{2 x} + 9) \frac{d y}{d x} = y

Frequently Asked Questions (FAQ)

What is the solution for e^yy^'=(x+e^y-1) ?
The solution for e^yy^'=(x+e^y-1) is y=ln(c_{1}-e^{-x}x)+x