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Beliebt Rechnen >

y^'=xln(x),y(1)=2

Lösung

y^{^{'}} = x ln (x), y (1) = 2

Lösung

y = \frac{x ^{2} ln ( x )}{2} - \frac{x ^{2}}{4} + \frac{9}{4}

Schritte zur Lösung

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

Wenn

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

dann

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}

Wende die Anfangsbedingung an:

y = \frac{x ^{2} ln ( x )}{2} - \frac{x ^{2}}{4} + \frac{9}{4}

y = \frac{x ^{2} ln ( x )}{2} - \frac{x ^{2}}{4} + \frac{9}{4}

Graph

Beliebte Beispiele

integral of x(2+x^3)^2

\int x (2 + x^{3})^{2} d x

integral of In^2

\int I n^{2} d x

integral of (1+cos(x))/(cos^2(x))

\int \frac{1 + cos ( x )}{cos ^{2} ( x )} d x

tangent f(x)=6x^2-6x,\at x=0

t an g e n t f (x) = 6 x^{2} - 6 x, at x = 0

(dx)/(dt)=(x^2-1)t,x(0)=0

\frac{d x}{d t} = (x^{2} - 1) t, x (0) = 0