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Popular >

y^'=xln(x)

Solution

y^{^{'}} = x ln (x)

Solution

y = \frac{1}{2} x^{2} ln (x) - \frac{x ^{2}}{4} + c_{1}

Solution steps

y^{'} (x) = x ln (x)

If

f^{^{'}} (x) = g (x)

then

f (x) = \int g (x) d x

y = \int x ln (x) d x

\int x ln (x) d x = \frac{1}{2} x^{2} ln (x) - \frac{x ^{2}}{4} + c_{1}

y = \frac{1}{2} x^{2} ln (x) - \frac{x ^{2}}{4} + c_{1}

Popular Examples

derivative of (8x/5)

\frac{d}{d x} (\frac{8 x}{5})

derivative of (3x^6+2x^3^4)

\frac{d}{d x} ((3 x^{6} + 2 x^{3})^{4})

integral of (2x+5)(x^2+5x)7

\int (2 x + 5) (x^{2} + 5 x) 7 d x

integral from 1 to n of xln(x)

\int_{1}^{n} x ln (x) d x

(\partial)/(\partial x)((x^2+y)e^{y/2})

\frac{\partial}{\partial x} ((x^{2} + y) e^{\frac{y}{2}})

Frequently Asked Questions (FAQ)

What is the solution for y^'=xln(x) ?
The solution for y^'=xln(x) is y= 1/2 x^2ln(x)-(x^2)/4+c_{1}