(dy)/(dx)=x^4(y-4),y(0)=8

Lösung

\frac{d y}{d x} = x^{4} (y - 4), y (0) = 8

y = 4 e^{\frac{x ^{5}}{5}} + 4

Schritte zur Lösung

\frac{d y}{d x} = x^{4} (y - 4)

Solve separable ODE:

y = 4 e^{\frac{x ^{5}}{5}} + 4

y = 4 e^{\frac{x ^{5}}{5}} + 4

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

e^{y} y^{^{'}} = 1

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

4 \cdot y^{^{'}} + y = 0

\frac{d y}{d t} = - \frac{y}{15 + t}