Internal problem ID [4063]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 29
Problem number: 824.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [[_homogeneous, `class G`]]
\[ \boxed {{y^{\prime }}^{2}+x y^{2} y^{\prime }+y^{3}=0} \]
✓ Solution by Maple
Time used: 0.156 (sec). Leaf size: 127
dsolve(diff(y(x),x)^2+x*y(x)^2*diff(y(x),x)+y(x)^3 = 0,y(x), singsol=all)
\begin{align*} y \left (x \right ) = \frac {4}{x^{2}} y \left (x \right ) = 0 y \left (x \right ) = \frac {2 \sqrt {2}\, x c_{1} -2 c_{1}^{2}}{c_{1}^{2} \left (c_{1}^{2}-2 x^{2}\right )} y \left (x \right ) = -\frac {2 \left (\sqrt {2}\, x c_{1} +c_{1}^{2}\right )}{c_{1}^{2} \left (c_{1}^{2}-2 x^{2}\right )} y \left (x \right ) = -\frac {\left (\sqrt {2}\, x c_{1} -2\right ) c_{1}^{2}}{2 \left (c_{1}^{2} x^{2}-2\right )} y \left (x \right ) = \frac {\left (\sqrt {2}\, x c_{1} +2\right ) c_{1}^{2}}{2 c_{1}^{2} x^{2}-4} \end{align*}
✓ Solution by Mathematica
Time used: 0.914 (sec). Leaf size: 71
DSolve[(y'[x])^2+x y[x]^2 y'[x]+y[x]^3==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {\cosh (c_1)-\sinh (c_1)}{-i x+\cosh (c_1)+\sinh (c_1)} y(x)\to \frac {\cosh (c_1)-\sinh (c_1)}{i x+\cosh (c_1)+\sinh (c_1)} y(x)\to 0 y(x)\to \frac {4}{x^2} \end{align*}