y^'=8x^6y-y,y(1)=-4

解答

y^{^{'}} = 8 x^{6} y - y, y (1) = - 4

y = - \frac{4}{7 e e ^{\frac{- 8 x ^{7} + 7 x}{7}}}

求解步骤

y^{'} (x) = 8 x^{6} y - y

求解线性方程:

y = - \frac{4}{7 e e ^{\frac{- 8 x ^{7} + 7 x}{7}}}

y = - \frac{4}{7 e e ^{\frac{- 8 x ^{7} + 7 x}{7}}}

d er i v a t i v e \frac{3 x}{x}

\int \frac{3}{( z ^{2} + 4 ) ( z + 1 ) ^{2}} d z

\int cos (x) sin (2 x) d x

x \to - 1 lim (\frac{x ^{7} + 1}{x + 1})

\int (x^{6} + 1) e^{x^{7} + 7 x} d x