What is the solution for y^{1/2}*(dy)/(dx)+y^{3/2}=1 ?

The solution for y^{1/2}*(dy)/(dx)+y^{3/2}=1 is y=(-e^{-(3x+c_{1})/2}+1)^{2/3}

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y^{1/2}*(dy)/(dx)+y^{3/2}=1

y^{\frac{1}{2}} \cdot \frac{d y}{d x} + y^{\frac{3}{2}} = 1

y = (- e^{- \frac{3 x + c _{1}}{2}} + 1)^{\frac{2}{3}}

Solution steps

y^{\frac{1}{2}} \cdot \frac{d y}{d x} + y^{\frac{3}{2}} = 1

Solve separable ODE:

y = (- e^{- \frac{3 x + c _{1}}{2}} + 1)^{\frac{2}{3}}

y = (- e^{- \frac{3 x + c _{1}}{2}} + 1)^{\frac{2}{3}}

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What is the solution for y^{1/2}*(dy)/(dx)+y^{3/2}=1 ?
The solution for y^{1/2}*(dy)/(dx)+y^{3/2}=1 is y=(-e^{-(3x+c_{1})/2}+1)^{2/3}