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Popular >

(y-x)e^x+(1+e^x)y^'=0,y(1)=1

Solution

(y - x) e^{x} + (1 + e^{x}) y^{^{'}} = 0, y (1) = 1

Solution

y = \frac{1}{1 + e ^{x}} + \frac{e}{1 + e ^{x}} + \frac{e ^{x} x}{1 + e ^{x}} - \frac{e ^{x}}{1 + e ^{x}}

Solution steps

(y - x) e^{x} + (1 + e^{x}) y^{'} (x) = 0

Solve exact ODE:

y = \frac{1}{1 + e ^{x}} + \frac{e}{1 + e ^{x}} + \frac{e ^{x} x}{1 + e ^{x}} - \frac{e ^{x}}{1 + e ^{x}}

y = \frac{1}{1 + e ^{x}} + \frac{e}{1 + e ^{x}} + \frac{e ^{x} x}{1 + e ^{x}} - \frac{e ^{x}}{1 + e ^{x}}

Popular Examples

implicit (dy)/(dx),50x^{1/3}y^{2/3}=600 implicit derivative

\frac{d y}{d x}, 50 x^{\frac{1}{3}} y^{\frac{2}{3}} = 600

f(x)=(4x)^{ln(4x)}

f (x) = (4 x)^{l n (4 x)}

integral from 1 to 2 of (13)/(x^3+3x)

\int_{1}^{2} \frac{13}{x ^{3} + 3 x} d x

limit as x approaches infinity of 2x^2-8

x \to \infty lim (2 x^{2} - 8)

limit as x approaches-1 of (\sqrt[3]{-1.1}+1)/(-1.1+1)

Frequently Asked Questions (FAQ)

What is the solution for (y-x)e^x+(1+e^x)y^'=0,y(1)=1 ?
The solution for (y-x)e^x+(1+e^x)y^'=0,y(1)=1 is y= 1/(1+e^x)+e/(1+e^x)+(e^xx)/(1+e^x)-(e^x)/(1+e^x)