y^{''}-4y^'+5y=cos^2(x)

Lösung

y^{^{''}} - 4 y^{^{'}} + 5 y = cos^{2} (x)

y = e^{2 x} (c_{1} cos (x) + c_{2} sin (x)) + e^{2 x} cos (x) \cdot \int - \frac{cos ^{2} ( x ) sin ( x )}{e ^{2 x}} d x + e^{2 x} sin (x) \cdot \int \frac{cos ^{3} ( x )}{e ^{2 x}} d x

Schritte zur Lösung

y^{''} (x) - 4 y^{'} (x) + 5 y = cos^{2} (x)

Solve linear ODE:

y = e^{2 x} (c_{1} cos (x) + c_{2} sin (x)) + e^{2 x} cos (x) \cdot \int - \frac{cos ^{2} ( x ) sin ( x )}{e ^{2 x}} d x + e^{2 x} sin (x) \cdot \int \frac{cos ^{3} ( x )}{e ^{2 x}} d x

y = e^{2 x} (c_{1} cos (x) + c_{2} sin (x)) + e^{2 x} cos (x) \cdot \int - \frac{cos ^{2} ( x ) sin ( x )}{e ^{2 x}} d x + e^{2 x} sin (x) \cdot \int \frac{cos ^{3} ( x )}{e ^{2 x}} d x

2 y^{^{''}} - 6 y = 2 x^{2} - x^{2} - x + 3

y^{^{''}} - 12 y^{^{'}} + 32 y = 4 cos (3 t)

y^{^{''}} - 2 y^{^{'}} + y = 4 e^{3 x}

y^{^{''}} - 4 y^{^{'}} + 20 y = 2 sin (3 t)

y^{^{''}} + 4 y = cos (4 x) + 2 sin (4 x)