Internal problem ID [2323]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 37, page 171
Problem number: 10.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [_quadrature]
\[ \boxed {y {y^{\prime }}^{2}+\left (y^{2}-x^{3}-y^{2} x \right ) y^{\prime }-x y \left (y^{2}+x^{2}\right )=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 48
dsolve(y(x)*diff(y(x),x)^2+(y(x)^2-x^3-x*y(x)^2)*diff(y(x),x)-x*y(x)*(x^2+y(x)^2)=0,y(x), singsol=all)
\begin{align*} y \left (x \right ) &= {\mathrm e}^{-x} c_{1} \\ y \left (x \right ) &= \sqrt {{\mathrm e}^{x^{2}} c_{1} -x^{2}-1} \\ y \left (x \right ) &= -\sqrt {{\mathrm e}^{x^{2}} c_{1} -x^{2}-1} \\ \end{align*}
✓ Solution by Mathematica
Time used: 14.233 (sec). Leaf size: 61
DSolve[y[x]*y'[x]^2+(y[x]^2-x^3-x*y[x]^2)*y'[x]-x*y[x]*(x^2+y[x]^2)==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 e^{-x} \\ y(x)\to -\sqrt {-x^2+c_1 e^{x^2}-1} \\ y(x)\to \sqrt {-x^2+c_1 e^{x^2}-1} \\ \end{align*}