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

Lösung

\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}

Schritte zur Lösung

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

Solve separable ODE:

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}

y^{^{'}} = \frac{e ^{x} ( y - 2 )}{3}

\frac{d y}{d x} = \frac{x y ^{3} - y ^{3}}{e ^{x}}

y^{^{'}} + \frac{x}{x ^{2} - 9} \cdot y = 0

\frac{d x}{d t} = 10 - \frac{x}{10}

y^{^{'}} = \frac{y}{x + x e ^{x}}