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

Lösung

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}

Schritte zur Lösung

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

Solve linear ODE:

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}

\frac{d ^{2} y}{d x ^{2}} + 3 \frac{d y}{d x} - 4 y = x^{2}

y^{^{''}} + 3 y^{^{'}} + 2 y = - 6 - 4 x - 7 x^{2} - 2 x^{3}

(D^{2} + 1) y = 12 cos^{2} (x)

(D^{2} + 3 D + 2) y = 1 + 3 x + x^{2}

y^{^{''}} - 4 y = cos (x) - sin (x)