Internal problem ID [11227]
Book: An elementary treatise on differential equations by Abraham Cohen. DC heath publishers.
1906
Section: Chapter IV, differential equations of the first order and higher degree than the first.
Article 28. Summary. Page 59
Problem number: Ex 3.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [[_homogeneous, `class G`], _rational]
\[ \boxed {x^{3} {y^{\prime }}^{2}+x^{2} y y^{\prime }=-1} \]
✓ Solution by Maple
Time used: 0.281 (sec). Leaf size: 53
dsolve(x^3*diff(y(x),x)^2+x^2*y(x)*diff(y(x),x)+1=0,y(x), singsol=all)
\begin{align*} y \left (x \right ) &= -\frac {2}{\sqrt {x}} \\ y \left (x \right ) &= \frac {2}{\sqrt {x}} \\ y \left (x \right ) &= \frac {c_{1}^{2} x +4}{2 c_{1} x} \\ y \left (x \right ) &= \frac {c_{1}^{2}+4 x}{2 c_{1} x} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.934 (sec). Leaf size: 77
DSolve[x^3*(y'[x])^2+x^2*y[x]*y'[x]+1==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {e^{-\frac {c_1}{2}} \left (x+16 e^{c_1}\right )}{4 x} \\ y(x)\to \frac {e^{-\frac {c_1}{2}} \left (x+16 e^{c_1}\right )}{4 x} \\ y(x)\to -\frac {2}{\sqrt {x}} \\ y(x)\to \frac {2}{\sqrt {x}} \\ \end{align*}