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Beliebt Rechnen >

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

Lösung

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

Lösung

y = c_{1} e^{\frac{( 3 + 5 ) x}{2}} + c_{2} e^{\frac{( 3 - 5 ) x}{2}} - \frac{2}{15} sin (2 x) + \frac{4}{15} cos (2 x)

Schritte zur Lösung

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

Solve linear ODE:

y = c_{1} e^{\frac{( 3 + 5 ) x}{2}} + c_{2} e^{\frac{( 3 - 5 ) x}{2}} - \frac{2}{15} sin (2 x) + \frac{4}{15} cos (2 x)

y = c_{1} e^{\frac{( 3 + 5 ) x}{2}} + c_{2} e^{\frac{( 3 - 5 ) x}{2}} - \frac{2}{15} sin (2 x) + \frac{4}{15} cos (2 x)

Graph

Beliebte Beispiele

(D+1)^3y=16(2x+3)^{-1}e^x

(D + 1)^{3} y = 16 (2 x + 3)^{- 1} e^{x}

y^{''}-4y^'-8y=8x^2+8x+1

y^{^{''}} - 4 y^{^{'}} - 8 y = 8 x^{2} + 8 x + 1

y^{^{''}} - 9 y = 63

solvefor D,D(x)=e^{2x^3+4}

so l v e f or D, D (x) = e^{2 x^{3} + 4}

y^{''}+3y^'-4y=12

y^{^{''}} + 3 y^{^{'}} - 4 y = 12