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人気のある微分積分 >

y^'= 1/2+1/4 sin(t)-y/(50)

解

y^{^{'}} = \frac{1}{2} + \frac{1}{4} sin (t) - \frac{y}{50}

解

y = 25 + \frac{25 ( sin ( t ) - 50 cos ( t ) )}{5002} + \frac{c _{1}}{e ^{\frac{t}{50}}}

解答ステップ

y^{'} (t) = \frac{1}{2} + \frac{1}{4} sin (t) - \frac{y}{50}

線形 ODE を解く:

y = 25 + \frac{25 ( sin ( t ) - 50 cos ( t ) )}{5002} + \frac{c _{1}}{e ^{\frac{t}{50}}}

y = 25 + \frac{25 ( sin ( t ) - 50 cos ( t ) )}{5002} + \frac{c _{1}}{e ^{\frac{t}{50}}}

グラフ

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