Internal problem ID [9154]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 819.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_1st_order, `_with_symmetry_[F(x),G(x)]`]]
\[ \boxed {y^{\prime }-\sqrt {x^{2}+3 y}-x^{2} \sqrt {x^{2}+3 y}-x^{3} \sqrt {x^{2}+3 y}=-\frac {2 x}{3}} \]
✓ Solution by Maple
Time used: 0.094 (sec). Leaf size: 30
dsolve(diff(y(x),x) = -2/3*x+(x^2+3*y(x))^(1/2)+x^2*(x^2+3*y(x))^(1/2)+x^3*(x^2+3*y(x))^(1/2),y(x), singsol=all)
\[ c_{1} +\frac {3 x^{4}}{8}+\frac {x^{3}}{2}+\frac {3 x}{2}-\sqrt {x^{2}+3 y \left (x \right )} = 0 \]
✓ Solution by Mathematica
Time used: 0.471 (sec). Leaf size: 63
DSolve[y'[x] == (-2*x)/3 + Sqrt[x^2 + 3*y[x]] + x^2*Sqrt[x^2 + 3*y[x]] + x^3*Sqrt[x^2 + 3*y[x]],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{192} \left (9 x^8+24 x^7+16 x^6+72 x^5+(96-72 c_1) x^4-96 c_1 x^3+80 x^2-288 c_1 x+144 c_1{}^2\right ) \]