y^'=t^{1/4}-y

解

y^{^{'}} = t^{\frac{1}{4}} - y

y = \frac{Γ ( \frac{1}{\frac{4}{5}} , - ( ( t ^{\frac{1}{4}} ) ^{5} ) ^{\frac{4}{5}} )}{( - 1 ) ^{\frac{1}{4}} e ^{t}} + \frac{c _{1}}{e ^{t}}

解答ステップ

y^{'} (t) = t^{\frac{1}{4}} - y

線形 ODE を解く:

y = \frac{Γ ( \frac{1}{\frac{4}{5}} , - ( ( t ^{\frac{1}{4}} ) ^{5} ) ^{\frac{4}{5}} )}{( - 1 ) ^{\frac{1}{4}} e ^{t}} + \frac{c _{1}}{e ^{t}}

y = \frac{Γ ( \frac{1}{\frac{4}{5}} , - ( ( t ^{\frac{1}{4}} ) ^{5} ) ^{\frac{4}{5}} )}{( - 1 ) ^{\frac{1}{4}} e ^{t}} + \frac{c _{1}}{e ^{t}}