(t^2+25)(dy)/(dt)+2ty=t^2(t^2+25)

解答

(t^{2} + 25) \frac{d y}{d t} + 2 t y = t^{2} (t^{2} + 25)

y = \frac{t ^{5}}{5 ( t ^{2} + 25 )} + \frac{25 t ^{3}}{3 ( t ^{2} + 25 )} + \frac{c _{1}}{t ^{2} + 25}

求解步骤

(t^{2} + 25) \frac{d y}{d t} + 2 t y = t^{2} (t^{2} + 25)

求解线性方程:

y = \frac{t ^{5}}{5 ( t ^{2} + 25 )} + \frac{25 t ^{3}}{3 ( t ^{2} + 25 )} + \frac{c _{1}}{t ^{2} + 25}

y = \frac{t ^{5}}{5 ( t ^{2} + 25 )} + \frac{25 t ^{3}}{3 ( t ^{2} + 25 )} + \frac{c _{1}}{t ^{2} + 25}

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