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Beliebt Rechnen >

(t^3+7t^3x^2)dt+xe^{t^4}dx=0,x(0)=0

Lösung

(t^{3} + 7 t^{3} x^{2}) d t + x e^{t^{4}} d x = 0, x (0) = 0

Lösung

x = \frac{e ^{\frac{7 e ^{- t^{4}} + c _{1}}{2}} - 1}{7}, x = - \frac{e ^{\frac{7 e ^{- t^{4}} + c _{1}}{2}} - 1}{7}

Schritte zur Lösung

(t^{3} + 7 t^{3} x^{2}) d t + x e^{t^{4}} d x = 0

Solve separable ODE:

x = \frac{e ^{\frac{7 e ^{- t^{4}} + c _{1}}{2}} - 1}{7}, x = - \frac{e ^{\frac{7 e ^{- t^{4}} + c _{1}}{2}} - 1}{7}

x = \frac{e ^{\frac{7 e ^{- t^{4}} + c _{1}}{2}} - 1}{7}, x = - \frac{e ^{\frac{7 e ^{- t^{4}} + c _{1}}{2}} - 1}{7}

Graph

Beliebte Beispiele

y^'=3(y-1)^{2/3}

y^{^{'}} = 3 (y - 1)^{\frac{2}{3}}

y^'+1/2 (x-2)y^2=0

y^{^{'}} + \frac{1}{2} (x - 2) y^{2} = 0

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

y^'=(11cos(11x))/(3+2y),y(0)=-1

y^{^{'}} = \frac{11 cos ( 11 x )}{3 + 2 y}, y (0) = - 1

(dy)/(dx)=(2x)(y)

\frac{d y}{d x} = (2 x) (y)