(dy)/(dx)= 1/x (y^2+0.6y)

解答

\frac{d y}{d x} = \frac{1}{x} (y^{2} + 0.6 y)

y = \frac{0.6 e ^{0.6 c_{1}} x ^{0.6}}{1 - e ^{0.6 c_{1}} x ^{0.6}}

求解步骤

\frac{d y}{d x} = \frac{1}{x} (y^{2} + 0.6 y)

求解可分离方程:

y = \frac{0.6 e ^{0.6 c_{1}} x ^{0.6}}{1 - e ^{0.6 c_{1}} x ^{0.6}}

y = \frac{0.6 e ^{0.6 c_{1}} x ^{0.6}}{1 - e ^{0.6 c_{1}} x ^{0.6}}

\int_{- 1}^{3} - x^{2} + 2 x + 3 d x

f^{^{'}} (x) = x (3 + 5 x), f (1) = 7

\int \frac{sin ( x )}{sin ( x ) + cos ( x )} d x

so l v e f or f, tan (f) (x) = 7 x^{4} + 4 \frac{x}{2} x^{3} + 1

\int (\frac{1}{x ^{3}} + \frac{7}{x ^{2}}) d x