3y^'-5e^{2x}y=0,y(0)=3

Lösung

3 y^{^{'}} - 5 e^{2 x} y = 0, y (0) = 3

y = 3 e^{\frac{5 e ^{2 x} - 5}{6}}

Schritte zur Lösung

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

Solve separable ODE:

y = 3 e^{\frac{5 e ^{2 x} - 5}{6}}

y = 3 e^{\frac{5 e ^{2 x} - 5}{6}}

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

y^{^{'}} = \frac{1}{y ^{1}}

\frac{d y}{d x} = 6 (5 - y)

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

y^{^{'}} = 1 + 4 y^{2}, y (0) = 0