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Beliebt Rechnen >

(1+x^2+y^2+x^2y^2)dy=(1+y^2)dx

Lösung

(1 + x^{2} + y^{2} + x^{2} y^{2}) d y = (1 + y^{2}) d x

Lösung

y = arctan (x) + c_{1}

Schritte zur Lösung

(1 + x^{2} + y^{2} + x^{2} y^{2}) d y = (1 + y^{2}) d x

Lass

y

die abhängige Variable sein. Teile durch

d x

:

(1 + x^{2} + y^{2} + x^{2} y^{2}) \frac{d y}{d x} = 1 + y^{2}

Ersetze

\frac{d y}{d x}

mit

y^{'} (x)

(1 + x^{2} + y^{2} + x^{2} y^{2}) y^{^{'}} (x) = 1 + y^{2}

Isoliere

y^{'} (x) : y^{'} (x) = \frac{1}{x ^{2} + 1}

Wenn

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

dann

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

y = \int \frac{1}{x ^{2} + 1} d x

\int \frac{1}{x ^{2} + 1} d x = arctan (x) + c_{1}

y = arctan (x) + c_{1}

Graph

Beliebte Beispiele

integral of (100)/(100-y)

\int \frac{100}{100 - y} d y

y^{'''}+4*y^'=3x-1

y^{^{'''}} + 4 \cdot y^{^{'}} = 3 x - 1

limit as x approaches 1 of e^{4x^5-4x}

x \to 1 lim (e^{4 x^{5} - 4 x})

(\partial)/(\partial x)(x^2y^3+2x^4y)

\frac{\partial}{\partial x} (x^{2} y^{3} + 2 x^{4} y)

derivative of 3x^4-5x^2+1

\frac{d}{d x} (3 x^{4} - 5 x^{2} + 1)