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人気のある微分積分 >

y^{'''}+y^'=sec(t),y^'(0)=3,y^{''}(0)=-2

解

y^{^{'''}} + y^{^{'}} = sec (t), y^{^{'}} (0) = 3, y^{^{''}} (0) = - 2

解

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

y = c_{1} + 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^2y)/(dx^2)-2*(dy)/(dx)+y=(x-1)*e^x

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

(d^2y)/(dx^2)+(dy)/(dx)=sin(x)

\frac{d ^{2} y}{d x ^{2}} + \frac{d y}{d x} = sin (x)

y^{''}-81y=e^{9x}

y^{^{''}} - 81 y = e^{9 x}

y^{''}+4y=t^2+7e^t,y(0)=0,y^'(0)=2

y^{^{''}} + 4 y = t^{2} + 7 e^{t}, y (0) = 0, y^{^{'}} (0) = 2

y^{''}+y^'=(3t^2+2t)e^t+cos(t/2)

y^{^{''}} + y^{^{'}} = (3 t^{2} + 2 t) e^{t} + cos (\frac{t}{2})