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Beliebt Rechnen >

sqrt(y)dx+(2+x)dy=0,y(-1)=4

Lösung

y d x + (2 + x) d y = 0, y (- 1) = 4

Lösung

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

Schritte zur Lösung

y d x + (2 + x) d y = 0

Solve separable ODE:

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

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

Graph

Beliebte Beispiele

y^{^{'}} = x y + x - y - 1

y^'+(2x)/(1+x^2)y=(-x)/(1+x^2)

y^{^{'}} + \frac{2 x}{1 + x ^{2}} y = \frac{- x}{1 + x ^{2}}

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

(dy)/(dx)=10xsqrt(25-y^2)

\frac{d y}{d x} = 10 x 25 - y^{2}

y^'=(13x)/(y+x^2y)

y^{^{'}} = \frac{13 x}{y + x ^{2} y}