(dy)/(dt)+(4y)/(200+3t)=8

解

\frac{d y}{d t} + \frac{4 y}{200 + 3 t} = 8

y = \frac{8 ( 21 t ( 200 + 3 t ) ^{\frac{4}{3}} - 4 ( ( 3 t + 200 ) ^{\frac{7}{3}} - 350 ( 3 t + 200 ) ^{\frac{4}{3}} ) )}{21 ( 200 + 3 t ) ^{\frac{4}{3}}} + \frac{c _{1}}{( 200 + 3 t ) ^{\frac{4}{3}}}

解答ステップ

\frac{d y}{d t} + \frac{4 y}{200 + 3 t} = 8

線形 ODE を解く:

y = \frac{8 ( 21 t ( 200 + 3 t ) ^{\frac{4}{3}} - 4 ( ( 3 t + 200 ) ^{\frac{7}{3}} - 350 ( 3 t + 200 ) ^{\frac{4}{3}} ) )}{21 ( 200 + 3 t ) ^{\frac{4}{3}}} + \frac{c _{1}}{( 200 + 3 t ) ^{\frac{4}{3}}}

y = \frac{8 ( 21 t ( 200 + 3 t ) ^{\frac{4}{3}} - 4 ( ( 3 t + 200 ) ^{\frac{7}{3}} - 350 ( 3 t + 200 ) ^{\frac{4}{3}} ) )}{21 ( 200 + 3 t ) ^{\frac{4}{3}}} + \frac{c _{1}}{( 200 + 3 t ) ^{\frac{4}{3}}}