y^{''}+b^2y=xcos(ax)

Lösung

y^{^{''}} + b^{2} y = x cos (a x)

y = c_{1} cos (b x) + c_{2} sin (b x) + \frac{x cos ( a x )}{b ^{2} - a ^{2}} + \frac{2 a sin ( a x )}{( b ^{2} - a ^{2} ) ^{2}}

Schritte zur Lösung

y^{''} (x) + b^{2} y = x cos (a x)

Solve linear ODE:

y = c_{1} cos (b x) + c_{2} sin (b x) + \frac{x cos ( a x )}{b ^{2} - a ^{2}} + \frac{2 a sin ( a x )}{( b ^{2} - a ^{2} ) ^{2}}

y = c_{1} cos (b x) + c_{2} sin (b x) + \frac{x cos ( a x )}{b ^{2} - a ^{2}} + \frac{2 a sin ( a x )}{( b ^{2} - a ^{2} ) ^{2}}

y^{^{''}} - y = cos (x)

y^{^{''}} + 2 y^{^{'}} - 3 y = tan (x)

\frac{d ^{2} y}{d x ^{2}} - 2 \frac{d y}{d x} + 5 y = e^{x} cos (2 x)

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

x^{^{''}} - 4 x^{^{'}} + 4 x = e^{2 t}, x (0) = 2, x^{^{'}} (0) = 1