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人気のある微分積分 >

y^{'''}+y^'=sec(t),y^'(0)=3

解

y^{^{'''}} + y^{^{'}} = sec (t), y^{^{'}} (0) = 3

解

y = c_{1} + c_{2} cos (t) + 3 sin (t) + ln (tan (t) + sec (t)) - t cos (t) + ln (cos (t)) sin (t)

解答ステップ

y^{'''} (t) + y^{'} (t) = sec (t)

線形 ODE を解く:

y = c_{1} + c_{2} cos (t) + 3 sin (t) + ln (tan (t) + sec (t)) - t cos (t) + ln (cos (t)) sin (t)

y = c_{1} + c_{2} cos (t) + 3 sin (t) + ln (tan (t) + sec (t)) - t cos (t) + ln (cos (t)) sin (t)

グラフ

人気の例

(d^2-2d)y=e^xsin(x)

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

1/2 y^{''}+2y=3tan(2t)-1/3 e^{4t}

\frac{1}{2} y^{^{''}} + 2 y = 3 tan (2 t) - \frac{1}{3} e^{4 t}

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

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

y^{''}-3y^'+3y^'-y=x-8e^x

y^{^{''}} - 3 y^{^{'}} + 3 y^{^{'}} - y = x - 8 e^{x}

y^{''}+100y^'+1/(0.0004)y=30,y(0)=0

y^{^{''}} + 100 y^{^{'}} + \frac{1}{0.0004} y = 30, y (0) = 0