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Popular >

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

Solution

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

Solution

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}

Solution steps

\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}

Graph

Popular Examples

y^'=(e^x(y-2))/3

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

(dy)/(dx)=(xy^3-y^3)/(e^x)

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

y^'+x/(x^2-9)*y=0

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

(dx)/(dt)=10-x/(10)

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

y^3((dy)/(dx))=2x^2y^4-6x^2

y^{3} (\frac{d y}{d x}) = 2 x^{2} y^{4} - 6 x^{2}

Frequently Asked Questions (FAQ)

What is the solution for (dy)/(dx)y=(x^6ln(x))^4 ?
The solution for (dy)/(dx)y=(x^6ln(x))^4 is