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Beliebt Rechnen >

(d^2-2d+2)y=x^2e^3x

Lösung

(d^{2} - 2 d + 2) y = x^{2} e^{3} x

Lösung

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

Schritte zur Lösung

(d^{2} - 2 d + 2) y = x^{2} e^{3} x

Solve linear ODE:

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

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

Graph

Beliebte Beispiele

y^{''}+y^'-2y=8sin(2x)

y^{^{''}} + y^{^{'}} - 2 y = 8 sin (2 x)

(d^2+2d+1)y=cos^2(x)

(d^{2} + 2 d + 1) y = cos^{2} (x)

(d^2+5d+6)y=e^{-2}xsin^2(x)

(d^{2} + 5 d + 6) y = e^{- 2} x sin^{2} (x)

solvefor y,(d^2+4d+4)y=sin(t)

so l v e f or y, (d^{2} + 4 d + 4) y = sin (t)

(d^2-1)y=e^x(1+x^2)

(d^{2} - 1) y = e^{x} (1 + x^{2})