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Popular >

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

Solution

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

Solution

y = - x^{3} + \frac{x ^{6}}{216} - \frac{x ^{5}}{12} + \frac{c _{1} x ^{4}}{36} + \frac{x ^{4}}{2} + \frac{- c _{1} x ^{3} - c _{1}^{2} x}{3} + \frac{c _{1}^{2} x ^{2}}{18} + c_{1} x^{2} + \frac{c _{1}^{3}}{27} - 1

Solution steps

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

Solve separable ODE:

y = - x^{3} + \frac{x ^{6}}{216} - \frac{x ^{5}}{12} + \frac{c _{1} x ^{4}}{36} + \frac{x ^{4}}{2} + \frac{- c _{1} x ^{3} - c _{1}^{2} x}{3} + \frac{c _{1}^{2} x ^{2}}{18} + c_{1} x^{2} + \frac{c _{1}^{3}}{27} - 1

y = - x^{3} + \frac{x ^{6}}{216} - \frac{x ^{5}}{12} + \frac{c _{1} x ^{4}}{36} + \frac{x ^{4}}{2} + \frac{- c _{1} x ^{3} - c _{1}^{2} x}{3} + \frac{c _{1}^{2} x ^{2}}{18} + c_{1} x^{2} + \frac{c _{1}^{3}}{27} - 1

Popular Examples

limit as x approaches 2+of e^{3/(2-x)}

x \to 2 + lim (e^{\frac{3}{2 - x}})

derivative of (x^3+y^3/(x^2+y^2))

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

\int 23

integral of (x+2)/(x^2(x^2+1))

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

sum from n=1 to infinity of 1/((2n-1)2n)

n = 1 \sum \infty \frac{1}{( 2 n - 1 ) 2 n}

Frequently Asked Questions (FAQ)

What is the solution for y^'=(x-3)(y+1)^{(2/3)} ?
The solution for y^'=(x-3)(y+1)^{(2/3)} is