(dy)/(dx)y=(x^6ln(x))^4

解

\frac{d y}{d x} y = (x^{6} ln (x))^{4}

y = \frac{781250 x ^{25} ln ^{4} ( x ) - 8 ( 15625 x ^{25} ln ^{3} ( x ) - 3 ( 625 x ^{25} ln ^{2} ( x ) - 2 ( 25 x ^{25} ln ( x ) - x ^{25} ) ) ) + c _{1}}{3125}, y = - \frac{781250 x ^{25} ln ^{4} ( x ) - 8 ( 15625 x ^{25} ln ^{3} ( x ) - 3 ( 625 x ^{25} ln ^{2} ( x ) - 2 ( 25 x ^{25} ln ( x ) - x ^{25} ) ) ) + c _{1}}{3125}

解答ステップ

\frac{d y}{d x} y = (x^{6} ln (x))^{4}

分離可能 ODE を解く:

y = \frac{781250 x ^{25} ln ^{4} ( x ) - 8 ( 15625 x ^{25} ln ^{3} ( x ) - 3 ( 625 x ^{25} ln ^{2} ( x ) - 2 ( 25 x ^{25} ln ( x ) - x ^{25} ) ) ) + c _{1}}{3125}, y = - \frac{781250 x ^{25} ln ^{4} ( x ) - 8 ( 15625 x ^{25} ln ^{3} ( x ) - 3 ( 625 x ^{25} ln ^{2} ( x ) - 2 ( 25 x ^{25} ln ( x ) - x ^{25} ) ) ) + c _{1}}{3125}

y = \frac{781250 x ^{25} ln ^{4} ( x ) - 8 ( 15625 x ^{25} ln ^{3} ( x ) - 3 ( 625 x ^{25} ln ^{2} ( x ) - 2 ( 25 x ^{25} ln ( x ) - x ^{25} ) ) ) + c _{1}}{3125}, y = - \frac{781250 x ^{25} ln ^{4} ( x ) - 8 ( 15625 x ^{25} ln ^{3} ( x ) - 3 ( 625 x ^{25} ln ^{2} ( x ) - 2 ( 25 x ^{25} ln ( x ) - x ^{25} ) ) ) + c _{1}}{3125}