y^{''}+5y=5sin(x),y(0)=1,y^'(0)=2

Lösung

y^{^{''}} + 5 y = 5 sin (x), y (0) = 1, y^{^{'}} (0) = 2

y = cos (5 x) + \frac{3}{4 5} sin (5 x) + \frac{5}{4} sin (x)

Schritte zur Lösung

y^{''} (x) + 5 y = 5 sin (x)

Solve linear ODE:

y = cos (5 x) + \frac{3}{4 5} sin (5 x) + \frac{5}{4} sin (x)

y = cos (5 x) + \frac{3}{4 5} sin (5 x) + \frac{5}{4} sin (x)

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

\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