y^{''}+3y=x^2sin(x)cos(x)

Lösung

y^{^{''}} + 3 y = x^{2} sin (x) cos (x)

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

Schritte zur Lösung

y^{''} (x) + 3 y = x^{2} sin (x) cos (x)

Solve linear ODE:

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

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

0.5 y^{^{''}} + 6 y^{^{'}} + 50 y = 24 sin (10 t)

y^{^{''}} + 2 y^{^{'}} + 2 y = 2

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

y^{^{''}} - 2 y^{^{'}} + 2 y = 1, y^{^{'}} 0 = 0

y^{^{''}} - 9 y = 9 e^{3 x} - 6 x^{4}