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Beliebt Rechnen >

y^{''}+4y=tcos(2t)

Lösung

y^{^{''}} + 4 y = t cos (2 t)

Lösung

y = c_{1} cos (2 t) + c_{2} sin (2 t) + \frac{t ^{2} sin ( 2 t )}{8} + \frac{t cos ( 2 t )}{16}

Schritte zur Lösung

y^{''} (t) + 4 y = t cos (2 t)

Solve linear ODE:

y = c_{1} cos (2 t) + c_{2} sin (2 t) + \frac{t ^{2} sin ( 2 t )}{8} + \frac{t cos ( 2 t )}{16}

y = c_{1} cos (2 t) + c_{2} sin (2 t) + \frac{t ^{2} sin ( 2 t )}{8} + \frac{t cos ( 2 t )}{16}

Graph

Beliebte Beispiele

y^{''}-2y^'-3y=5e^4x,y(0)=1,y^'(0)=0

y^{^{''}} - 2 y^{^{'}} - 3 y = 5 e^{4} x, y (0) = 1, y^{^{'}} (0) = 0

9y^{''}+4y=3x+12e^{-x}

9 y^{^{''}} + 4 y = 3 x + 12 e^{- x}

y^{''''}+8y^{''}+16y=-sin(x)

y^{^{''''}} + 8 y^{^{''}} + 16 y = - sin (x)

x^{''}+6x^'+23x=12cos(4t)

x^{^{''}} + 6 x^{^{'}} + 23 x = 12 cos (4 t)

(d^2+9)y=30sin^3(x)

(d^{2} + 9) y = 30 sin^{3} (x)