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Beliebt Rechnen >

(dy)/(dx)=2e^{x-y},y(0)=ln(4)

Lösung

\frac{d y}{d x} = 2 e^{x - y}, y (0) = ln (4)

Lösung

y = ln (2 e^{x} + 2)

Schritte zur Lösung

\frac{d y}{d x} = 2 e^{x - y}

Solve separable ODE:

y = ln (2 e^{x} + 2)

y = ln (2 e^{x} + 2)

Graph

Beliebte Beispiele

(dy)/(dx)=(4y)/(1+x)

\frac{d y}{d x} = \frac{4 y}{1 + x}

y^'=((2y+3))/(x^2)

y^{^{'}} = \frac{( 2 y + 3 )}{x ^{2}}

(dy)/(dx)=2*(x^2)*(y^2)

\frac{d y}{d x} = 2 \cdot (x^{2}) \cdot (y^{2})

dx-(dy)/(1+y^2)=0

d x - \frac{d y}{1 + y ^{2}} = 0

(dy)/(dx)=(2xy)/(x^2+1),y(1)=2

\frac{d y}{d x} = \frac{2 x y}{x ^{2} + 1}, y (1) = 2