3y^'-3e^{2x}y=0,y(0)=1

Lösung

3 y^{^{'}} - 3 e^{2 x} y = 0, y (0) = 1

y = e^{\frac{1}{2} e^{2 x} - \frac{1}{2}}

Schritte zur Lösung

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

Solve separable ODE:

y = e^{\frac{1}{2} e^{2 x} - \frac{1}{2}}

y = e^{\frac{1}{2} e^{2 x} - \frac{1}{2}}

\frac{d x}{d t} = t (x - 2)

\frac{d y}{d x} = \frac{8 sin ( x )}{sin ( y )}, y (0) = \frac{π}{2}

\frac{d}{d t} ((y) (8 y - y^{2})) = - \frac{8}{144} y, y (0) = 8

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

y^{^{'}} sec (x) = y^{2}, y (\frac{13 π}{2}) = \frac{1}{3}