Internal problem ID [9253]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 919.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_1st_order, _with_linear_symmetries], _rational]
\[ \boxed {y^{\prime }-\frac {y^{\frac {3}{2}} \left (x -y+\sqrt {y}\right )}{y^{\frac {3}{2}} x -y^{\frac {5}{2}}+y^{2}+x^{3}-3 y x^{2}+3 y^{2} x -y^{3}}=0} \]
✓ Solution by Maple
Time used: 0.046 (sec). Leaf size: 191
dsolve(diff(y(x),x) = y(x)^(3/2)*(x-y(x)+y(x)^(1/2))/(y(x)^(3/2)*x-y(x)^(5/2)+y(x)^2+x^3-3*x^2*y(x)+3*x*y(x)^2-y(x)^3),y(x), singsol=all)
\[ -\frac {\left (c_{1} x^{6}+80 x^{3}-54 x^{2}-12 x -1\right ) y \left (x \right )^{\frac {7}{2}}+\left (-6 c_{1} x^{5}-60 x^{2}+36 x +6\right ) y \left (x \right )^{\frac {9}{2}}+\left (15 c_{1} x^{4}+24 x -9\right ) y \left (x \right )^{\frac {11}{2}}+\left (-60 x^{4}+36 x^{3}+6 x^{2}\right ) y \left (x \right )^{\frac {5}{2}}+\left (-20 c_{1} x^{3}-4\right ) y \left (x \right )^{\frac {13}{2}}+\left (24 x^{5}-9 x^{4}\right ) y \left (x \right )^{\frac {3}{2}}+15 y \left (x \right )^{\frac {15}{2}} c_{1} x^{2}-6 y \left (x \right )^{\frac {17}{2}} c_{1} x +y \left (x \right )^{\frac {19}{2}} c_{1} -4 x^{6} \sqrt {y \left (x \right )}+12 \left (x -y \left (x \right )\right )^{3} \left (y \left (x \right )^{2}+\left (-2 x -\frac {1}{3}\right ) y \left (x \right )+x^{2}\right ) y \left (x \right )}{y \left (x \right )^{\frac {7}{2}} \left (x -y \left (x \right )\right )^{6}} = 0 \]
✓ Solution by Mathematica
Time used: 55.594 (sec). Leaf size: 251
DSolve[y'[x] == ((x + Sqrt[y[x]] - y[x])*y[x]^(3/2))/(x^3 - 3*x^2*y[x] + x*y[x]^(3/2) + y[x]^2 + 3*x*y[x]^2 - y[x]^(5/2) - y[x]^3),y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \text {Root}\left [\text {$\#$1}^9 c_1{}^4-6 \text {$\#$1}^8 c_1{}^4 x+\text {$\#$1}^7 \left (15 c_1{}^4 x^2-6 c_1{}^2\right )+\text {$\#$1}^6 \left (-20 c_1{}^4 x^3+30 c_1{}^2 x-4+2 c_1{}^2\right )+\text {$\#$1}^5 \left (15 c_1{}^4 x^4-60 c_1{}^2 x^2+24 x-6 c_1{}^2 x+9\right )+\text {$\#$1}^4 \left (-6 c_1{}^4 x^5+60 c_1{}^2 x^3-60 x^2+6 c_1{}^2 x^2-36 x-6\right )+\text {$\#$1}^3 \left (c_1{}^4 x^6-30 c_1{}^2 x^4+80 x^3-2 c_1{}^2 x^3+54 x^2+12 x+1\right )+\text {$\#$1}^2 \left (6 c_1{}^2 x^5-60 x^4-36 x^3-6 x^2\right )+\text {$\#$1} \left (24 x^5+9 x^4\right )-4 x^6\&,1\right ] \]