Internal problem ID [4188]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 32
Problem number: 954.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [[_homogeneous, `class A`], _rational, _dAlembert]
\[ \boxed {\left (y+x \right ) {y^{\prime }}^{2}+2 x y^{\prime }-y=0} \]
✓ Solution by Maple
Time used: 0.297 (sec). Leaf size: 121
dsolve((x+y(x))*diff(y(x),x)^2+2*x*diff(y(x),x)-y(x) = 0,y(x), singsol=all)
\begin{align*} y \left (x \right ) &= -\frac {\left (1+i \sqrt {3}\right ) x}{2} \\ y \left (x \right ) &= \frac {\left (i \sqrt {3}-1\right ) x}{2} \\ \ln \left (x \right )-\operatorname {arctanh}\left (\frac {y \left (x \right )+2 x}{2 x \sqrt {\frac {y \left (x \right )^{2}+x y \left (x \right )+x^{2}}{x^{2}}}}\right )+\ln \left (\frac {y \left (x \right )}{x}\right )-c_{1} &= 0 \\ \ln \left (x \right )+\operatorname {arctanh}\left (\frac {y \left (x \right )+2 x}{2 x \sqrt {\frac {y \left (x \right )^{2}+x y \left (x \right )+x^{2}}{x^{2}}}}\right )+\ln \left (\frac {y \left (x \right )}{x}\right )-c_{1} &= 0 \\ \end{align*}
✓ Solution by Mathematica
Time used: 4.545 (sec). Leaf size: 166
DSolve[(x+y[x]) (y'[x])^2+2 x y'[x]-y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {2}{3} \sqrt {e^{c_1} \left (-3 x+e^{c_1}\right )}-\frac {e^{c_1}}{3} \\ y(x)\to \frac {2}{3} \sqrt {e^{c_1} \left (-3 x+e^{c_1}\right )}-\frac {e^{c_1}}{3} \\ y(x)\to e^{c_1}-2 \sqrt {e^{c_1} \left (x+e^{c_1}\right )} \\ y(x)\to 2 \sqrt {e^{c_1} \left (x+e^{c_1}\right )}+e^{c_1} \\ y(x)\to 0 \\ y(x)\to -\frac {1}{2} i \left (\sqrt {3}-i\right ) x \\ y(x)\to \frac {1}{2} i \left (\sqrt {3}+i\right ) x \\ \end{align*}