e^yy^'=((ln(t))^2)/t ,y(1)=ln(8)

Lösung

e^{y} y^{^{'}} = \frac{( ln ( t ) ) ^{2}}{t}, y (1) = ln (8)

y = ln (\frac{ln ^{3} ( t )}{3} + 8)

Schritte zur Lösung

e^{y} y^{'} (t) = \frac{( ln ( t ) ) ^{2}}{t}

Solve separable ODE:

y = ln (\frac{ln ^{3} ( t )}{3} + 8)

y = ln (\frac{ln ^{3} ( t )}{3} + 8)

y^{^{'}} = - (x + 2) y^{2}

(3 t^{2} + 5) y^{^{'}} = 3 t y, y (0) = 8

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

y^{^{'}} = e^{4 y + 7 t}

\frac{d y}{d x} = - ln ∣ x ∣ y