(dy)/(dx)y=e^{6x}sin(x)

Lösung

\frac{d y}{d x} y = e^{6 x} sin (x)

y = \frac{- 2 e ^{6 x} cos ( x ) + 12 e ^{6 x} sin ( x ) + c _{1}}{37}, y = - \frac{- 2 e ^{6 x} cos ( x ) + 12 e ^{6 x} sin ( x ) + c _{1}}{37}

Schritte zur Lösung

\frac{d y}{d x} y = e^{6 x} sin (x)

Solve separable ODE:

y = \frac{- 2 e ^{6 x} cos ( x ) + 12 e ^{6 x} sin ( x ) + c _{1}}{37}, y = - \frac{- 2 e ^{6 x} cos ( x ) + 12 e ^{6 x} sin ( x ) + c _{1}}{37}

y = \frac{- 2 e ^{6 x} cos ( x ) + 12 e ^{6 x} sin ( x ) + c _{1}}{37}, y = - \frac{- 2 e ^{6 x} cos ( x ) + 12 e ^{6 x} sin ( x ) + c _{1}}{37}

y^{^{'}} + cy = 0

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

2 x y + 4 x + (x^{2} - 4) \frac{d y}{d x} = 0

(1 - x^{2}) \frac{d y}{d x} - 2 x \frac{d y}{d x} + 3 y = 0

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