y^{''}+9y=x^2sin(4x)

Lösung

y^{^{''}} + 9 y = x^{2} sin (4 x)

y = c_{1} cos (3 x) + c_{2} sin (3 x) - \frac{x ^{2} sin ( 4 x )}{7} - \frac{16 x cos ( 4 x )}{49} + \frac{114}{343} sin (4 x)

Schritte zur Lösung

y^{''} (x) + 9 y = x^{2} sin (4 x)

Solve linear ODE:

y = c_{1} cos (3 x) + c_{2} sin (3 x) - \frac{x ^{2} sin ( 4 x )}{7} - \frac{16 x cos ( 4 x )}{49} + \frac{114}{343} sin (4 x)

y = c_{1} cos (3 x) + c_{2} sin (3 x) - \frac{x ^{2} sin ( 4 x )}{7} - \frac{16 x cos ( 4 x )}{49} + \frac{114}{343} sin (4 x)

y^{^{''}} - y^{^{'}} - 6 y = 12 x - e^{x}, y (0) = 1

\frac{d ^{2} y}{d x ^{2}} - 3 \frac{d y}{d x} + 2 y = 2 x

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

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

y^{^{''}} - 4 y^{^{'}} + 3 y = 13 cos (2 x)