d^2y=(2x^2+4)(x^2+3x)^4

解

d^{2} y = (2 x^{2} + 4) (x^{2} + 3 x)^{4}

y = c_{1} + c_{2} x + \frac{x ^{12}}{66} + \frac{12 x ^{11}}{55} + \frac{56 x ^{10}}{45} + \frac{11 x ^{9}}{3} + \frac{27 x ^{8}}{4} + \frac{72 x ^{7}}{7} + \frac{54 x ^{6}}{5}

解答ステップ

d^{2} y = (2 x^{2} + 4) (x^{2} + 3 x)^{4}

線形 ODE を解く:

y = c_{1} + c_{2} x + \frac{x ^{12}}{66} + \frac{12 x ^{11}}{55} + \frac{56 x ^{10}}{45} + \frac{11 x ^{9}}{3} + \frac{27 x ^{8}}{4} + \frac{72 x ^{7}}{7} + \frac{54 x ^{6}}{5}

y = c_{1} + c_{2} x + \frac{x ^{12}}{66} + \frac{12 x ^{11}}{55} + \frac{56 x ^{10}}{45} + \frac{11 x ^{9}}{3} + \frac{27 x ^{8}}{4} + \frac{72 x ^{7}}{7} + \frac{54 x ^{6}}{5}