Internal problem ID [4066]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 29
Problem number: 827.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [[_homogeneous, `class G`]]
\[ \boxed {{y^{\prime }}^{2}+2 x y^{3} y^{\prime }+y^{4}=0} \]
✓ Solution by Maple
Time used: 0.109 (sec). Leaf size: 48
dsolve(diff(y(x),x)^2+2*x*y(x)^3*diff(y(x),x)+y(x)^4 = 0,y(x), singsol=all)
\begin{align*} y \left (x \right ) &= -\frac {1}{x} \\ y \left (x \right ) &= \frac {1}{x} \\ y \left (x \right ) &= 0 \\ y \left (x \right ) &= \frac {1}{\sqrt {-c_{1} \left (-2 x +c_{1} \right )}} \\ y \left (x \right ) &= -\frac {1}{\sqrt {c_{1} \left (-c_{1} +2 x \right )}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.852 (sec). Leaf size: 161
DSolve[(y'[x])^2+2 x y[x]^3 y'[x]+y[x]^4==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} \text {Solve}\left [-\frac {\sqrt {x^2 y(x)^2-1} y(x)^2 \text {arctanh}\left (\frac {x y(x)}{\sqrt {x^2 y(x)^2-1}}\right )}{\sqrt {y(x)^4 \left (x^2 y(x)^2-1\right )}}-\log (y(x))&=c_1,y(x)\right ] \\ \text {Solve}\left [\frac {y(x)^2 \sqrt {x^2 y(x)^2-1} \text {arctanh}\left (\frac {x y(x)}{\sqrt {x^2 y(x)^2-1}}\right )}{\sqrt {y(x)^4 \left (x^2 y(x)^2-1\right )}}-\log (y(x))&=c_1,y(x)\right ] \\ y(x)\to 0 \\ y(x)\to -\frac {1}{x} \\ y(x)\to \frac {1}{x} \\ \end{align*}