(dy)/(dx)=10e^{5x-3y},y(0)=0

Lösung

\frac{d y}{d x} = 10 e^{5 x - 3 y}, y (0) = 0

y = \frac{ln ( 6 e ^{5 x} - 5 )}{3}

Schritte zur Lösung

\frac{d y}{d x} = 10 e^{5 x - 3 y}

Solve separable ODE:

y = \frac{ln ( 6 e ^{5 x} - 5 )}{3}

y = \frac{ln ( 6 e ^{5 x} - 5 )}{3}

y^{^{'}} + \frac{4}{x} y = 0

(1 + x) y d x + x d y = 0

\frac{d y}{d x} = \frac{7 x ^{2}}{y ^{3}}

2 \frac{d y}{d t} + 2 y = 3

\frac{d V}{d t} = 10 - \frac{2 V}{100}