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Beliebt Rechnen >

y^{''}-4y^'+7y=te^t

Lösung

y^{^{''}} - 4 y^{^{'}} + 7 y = t e^{t}

Lösung

y = e^{2 t} (c_{1} cos (3 t) + c_{2} sin (3 t)) + \frac{e ^{t} t}{4} + \frac{1}{8} e^{t}

Schritte zur Lösung

y^{''} (t) - 4 y^{'} (t) + 7 y = t e^{t}

Solve linear ODE:

y = e^{2 t} (c_{1} cos (3 t) + c_{2} sin (3 t)) + \frac{e ^{t} t}{4} + \frac{1}{8} e^{t}

y = e^{2 t} (c_{1} cos (3 t) + c_{2} sin (3 t)) + \frac{e ^{t} t}{4} + \frac{1}{8} e^{t}

Graph

Beliebte Beispiele

f(x)=(2xln(x)+x^2-1)/(x-1)

f (x) = \frac{2 x ln ( x ) + x ^{2} - 1}{x - 1}

limit as x approaches 0+of (1+x)^{5/x}

x \to 0 + lim ((1 + x)^{\frac{5}{x}})

(dy)/(dt)=-3(y-4)

\frac{d y}{d t} = - 3 (y - 4)

integral of 5z^3e^z

\int 5 z^{3} e^{z} d z

tangent f(x)=8x^3,\at x= 1/2

t an g e n t f (x) = 8 x^{3}, at x = \frac{1}{2}