(dy)/(dt)-ty=y,y(1)=3

Lösung

\frac{d y}{d t} - t y = y, y (1) = 3

y = 3 e^{t + \frac{t ^{2} - 3}{2}}

Schritte zur Lösung

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

Solve separable ODE:

y = 3 e^{t + \frac{t ^{2} - 3}{2}}

y = 3 e^{t + \frac{t ^{2} - 3}{2}}

y^{^{'}} = y^{- \frac{1}{3}}

\frac{d y}{d x} = \frac{5 e ^{x}}{e ^{y}}

y^{^{'}} = \frac{x}{y + 1}, y (2) = - 2

\frac{d y}{d t} = \frac{t}{t ^{2} y + y}, y (0) = 8

4 y^{^{'}} + 16 y = 8