(dy)/(dx)+3x^2y=x

Lösung

\frac{d y}{d x} + 3 x^{2} y = x

y = - \frac{Γ ( \frac{1}{\frac{3}{2}} , - ( x ^{2} ) ^{\frac{3}{2}} )}{3 e ^{x^{3}}} + \frac{c _{1}}{e ^{x^{3}}}

Schritte zur Lösung

\frac{d y}{d x} + 3 x^{2} y = x

Solve linear ODE:

y = - \frac{Γ ( \frac{1}{\frac{3}{2}} , - ( x ^{2} ) ^{\frac{3}{2}} )}{3 e ^{x^{3}}} + \frac{c _{1}}{e ^{x^{3}}}

y = - \frac{Γ ( \frac{1}{\frac{3}{2}} , - ( x ^{2} ) ^{\frac{3}{2}} )}{3 e ^{x^{3}}} + \frac{c _{1}}{e ^{x^{3}}}

x \to 1 lim (x^{4} - x^{2} + 2)

x \to 1 + lim (2^{\frac{1}{x - 1}})

x \to 1 lim (7 x + a)

y^{^{'}} = \frac{2 y}{x}, y (2) = 4

(2 y^{2} + 6 x) d x + 2 x y d y = 0