(dy)/(dx)= 1/7 (y)^{1/2}(cos(y^{1/2}))^2

解

\frac{d y}{d x} = \frac{1}{7} (y)^{\frac{1}{2}} (cos (y^{\frac{1}{2}}))^{2}

y = arctan^{2} (\frac{x + c _{1}}{14}) + 2 πn arctan (\frac{x + c _{1}}{14}) + π^{2} n^{2}

解答ステップ

\frac{d y}{d x} = \frac{1}{7} (y)^{\frac{1}{2}} (cos (y^{\frac{1}{2}}))^{2}

分離可能 ODE を解く:

y = arctan^{2} (\frac{x + c _{1}}{14}) + 2 πn arctan (\frac{x + c _{1}}{14}) + π^{2} n^{2}

y = arctan^{2} (\frac{x + c _{1}}{14}) + 2 πn arctan (\frac{x + c _{1}}{14}) + π^{2} n^{2}