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شائع >

y^{''}-8y^'+16y=t^{-7}e^{4t}

الحلّ

y^{^{''}} - 8 y^{^{'}} + 16 y = t^{- 7} e^{4 t}

الحلّ

y = c_{1} e^{4 t} + c_{2} t e^{4 t} + \frac{e ^{4 t}}{30 t ^{5}}

خطوات الحلّ

y^{''} (t) - 8 y^{'} (t) + 16 y = t^{- 7} e^{4 t}

Solve linear ODE:

y = c_{1} e^{4 t} + c_{2} t e^{4 t} + \frac{e ^{4 t}}{30 t ^{5}}

y = c_{1} e^{4 t} + c_{2} t e^{4 t} + \frac{e ^{4 t}}{30 t ^{5}}

أمثلة شائعة

limit as x approaches 1+of x^2

x \to 1 + lim (x^{2})

limit as x approaches 5 of x/(x-5)

x \to 5 lim (\frac{x}{x - 5})

integral of 1/(y^{1/3)}

\int \frac{1}{y ^{\frac{1}{3}}} d y

(x-1)y^'+(2x+1)y=0

(x - 1) y^{^{'}} + (2 x + 1) y = 0

d/(ds)(ln((s-1)/(s^2+2s+5)))

\frac{d}{d s} (ln (\frac{s - 1}{s ^{2} + 2 s + 5}))