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Beliebt Rechnen >

((sqrt(x)+x)dy)/(dx)=sqrt(y)+y

Lösung

\frac{( x + x ) d y}{d x} = y + y

Lösung

y = 2 e^{c_{1}} x + e^{c_{1}} x - 2 e^{\frac{c _{1}}{2}} x + e^{c_{1}} - 2 e^{\frac{c _{1}}{2}} + 1

Schritte zur Lösung

\frac{( x + x ) d y}{d x} = y + y

Solve separable ODE:

y = 2 e^{c_{1}} x + e^{c_{1}} x - 2 e^{\frac{c _{1}}{2}} x + e^{c_{1}} - 2 e^{\frac{c _{1}}{2}} + 1

y = 2 e^{c_{1}} x + e^{c_{1}} x - 2 e^{\frac{c _{1}}{2}} x + e^{c_{1}} - 2 e^{\frac{c _{1}}{2}} + 1

Graph

Beliebte Beispiele

derivative f(x)=x^2-4

d er i v a t i v e f (x) = x^{2} - 4

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

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

tangent 7x-4sqrt(x)

t an g e n t 7 x - 4 x

y^{^{'}} - y^{\frac{5}{3}} = 0

integral of x/(x-20)

\int \frac{x}{x - 20} d x