(dy)/(dx)=xsqrt(y)cos^2(sqrt(y))

解答

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

y = arctan^{2} (\frac{x ^{2} + 2 c _{1}}{4}) + 2 πn arctan (\frac{x ^{2} + 2 c _{1}}{4}) + π^{2} n^{2}

求解步骤

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

求解可分离方程:

y = arctan^{2} (\frac{x ^{2} + 2 c _{1}}{4}) + 2 πn arctan (\frac{x ^{2} + 2 c _{1}}{4}) + π^{2} n^{2}

y = arctan^{2} (\frac{x ^{2} + 2 c _{1}}{4}) + 2 πn arctan (\frac{x ^{2} + 2 c _{1}}{4}) + π^{2} n^{2}

\frac{\partial}{\partial x} (15 - x^{2} - 2 y^{2})

(\frac{d y}{d x}) = \frac{( x ^{2} ( y ^{5} - 2 ) )}{y ^{4}}

\int_{0}^{\frac{π}{4}} (sin (4 x)) d x

a re a x^{3} - 12 x^{2} + 20 x, - x^{3} + 12 x^{2} - 20 x

f (x) = 7 tan (x)