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Popular >

xyy^'=(y^2-1)^{3/2}

Solution

x y y^{^{'}} = (y^{2} - 1)^{\frac{3}{2}}

Solution

y = \frac{1 + ln ^{2} ( x ) + 2 c _{1} ln ( x ) + c _{1}^{2}}{ln ^{2} ( x ) + 2 c _{1} ln ( x ) + c _{1}^{2}}, y = - \frac{1 + ln ^{2} ( x ) + 2 c _{1} ln ( x ) + c _{1}^{2}}{ln ^{2} ( x ) + 2 c _{1} ln ( x ) + c _{1}^{2}}

Solution steps

x y y^{'} (x) = (y^{2} - 1)^{\frac{3}{2}}

Solve separable ODE:

y = \frac{1 + ln ^{2} ( x ) + 2 c _{1} ln ( x ) + c _{1}^{2}}{ln ^{2} ( x ) + 2 c _{1} ln ( x ) + c _{1}^{2}}, y = - \frac{1 + ln ^{2} ( x ) + 2 c _{1} ln ( x ) + c _{1}^{2}}{ln ^{2} ( x ) + 2 c _{1} ln ( x ) + c _{1}^{2}}

y = \frac{1 + ln ^{2} ( x ) + 2 c _{1} ln ( x ) + c _{1}^{2}}{ln ^{2} ( x ) + 2 c _{1} ln ( x ) + c _{1}^{2}}, y = - \frac{1 + ln ^{2} ( x ) + 2 c _{1} ln ( x ) + c _{1}^{2}}{ln ^{2} ( x ) + 2 c _{1} ln ( x ) + c _{1}^{2}}

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Frequently Asked Questions (FAQ)

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