y^{'''}+y^'=sec(t),y^'(0)=3,y^{''}(0)=-2

Lösung

y^{^{'''}} + y^{^{'}} = sec (t), y^{^{'}} (0) = 3, y^{^{''}} (0) = - 2

y = c_{1} + 2 cos (t) + 3 sin (t) + ln (tan (t) + sec (t)) - t cos (t) + ln (cos (t)) sin (t)

Schritte zur Lösung

y^{'''} (t) + y^{'} (t) = sec (t)

Solve linear ODE:

y = c_{1} + 2 cos (t) + 3 sin (t) + ln (tan (t) + sec (t)) - t cos (t) + ln (cos (t)) sin (t)

y = c_{1} + 2 cos (t) + 3 sin (t) + ln (tan (t) + sec (t)) - t cos (t) + ln (cos (t)) sin (t)

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

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

y^{^{''}} - 81 y = e^{9 x}

y^{^{''}} + 4 y = t^{2} + 7 e^{t}, y (0) = 0, y^{^{'}} (0) = 2

y^{^{''}} + y^{^{'}} = (3 t^{2} + 2 t) e^{t} + cos (\frac{t}{2})