y^'=e^y5^x,y(0)=ln(ln(5))

Lösung

y^{^{'}} = e^{y} 5^{x}, y (0) = ln (ln (5))

y = - ln (\frac{- 5 ^{x} + 2}{ln ( 5 )})

Schritte zur Lösung

y^{'} (x) = e^{y} 5^{x}

Solve separable ODE:

y = - ln (\frac{- 5 ^{x} + 2}{ln ( 5 )})

y = - ln (\frac{- 5 ^{x} + 2}{ln ( 5 )})

y^{^{'}} = - 10 x^{2} y

x^{3} y^{^{'}} + (5 x^{2} - 8) y = 0

3 y^{^{'}} - y = 0

y^{^{'}} + cos (t) y = cos (t)

\frac{d y}{d x} = \frac{x}{2 y x + y}