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人気のある微分積分 >

ydy=4xsqrt(y^2+1)dx

解

y d y = 4 x y^{2} + 1 d x

解

y = 4 x^{4} + 4 c_{1} x^{2} + c_{1}^{2} - 1, y = - 4 x^{4} + 4 c_{1} x^{2} + c_{1}^{2} - 1

解答ステップ

y d y = 4 x y^{2} + 1 d x

分離可能 ODE を解く:

y = 4 x^{4} + 4 c_{1} x^{2} + c_{1}^{2} - 1, y = - 4 x^{4} + 4 c_{1} x^{2} + c_{1}^{2} - 1

y = 4 x^{4} + 4 c_{1} x^{2} + c_{1}^{2} - 1, y = - 4 x^{4} + 4 c_{1} x^{2} + c_{1}^{2} - 1

グラフ

人気の例

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

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

(x/(x^2+y^4))dx+(((2y^3))/(x^2+y^4))dy=0

(\frac{x}{x ^{2} + y ^{4}}) d x + (\frac{( 2 y ^{3} )}{x ^{2} + y ^{4}}) d y = 0

derivative of (7x^3+x/(6sqrt(x)))

\frac{d}{d x} (\frac{7 x ^{3} + x}{6 x})

derivative of log_{10}(1/x)

\frac{d}{d x} (lo g_{10} (\frac{1}{x}))

y^{^{''}} - 6 y^{^{'}} = 4 x