Internal problem ID [3672]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 32
Problem number: 946.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [[_homogeneous, class A], _rational, _dAlembert]
Solve \begin {gather*} \boxed {y \left (y^{\prime }\right )^{2}+a x y^{\prime }+b y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.178 (sec). Leaf size: 107
dsolve(y(x)*diff(y(x),x)^2+a*x*diff(y(x),x)+b*y(x) = 0,y(x), singsol=all)
\begin{align*} y \relax (x ) = 0 \\ y \relax (x ) = \RootOf \left (-2 \ln \relax (x )+\int _{}^{\textit {\_Z}}\frac {-2 \textit {\_a}^{2}-a +\sqrt {-4 \textit {\_a}^{2} b +a^{2}}}{\textit {\_a} \left (\textit {\_a}^{2}+a +b \right )}d \textit {\_a} +2 c_{1}\right ) x \\ y \relax (x ) = \RootOf \left (-2 \ln \relax (x )-\left (\int _{}^{\textit {\_Z}}\frac {2 \textit {\_a}^{2}+\sqrt {-4 \textit {\_a}^{2} b +a^{2}}+a}{\textit {\_a} \left (\textit {\_a}^{2}+a +b \right )}d \textit {\_a} \right )+2 c_{1}\right ) x \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.643 (sec). Leaf size: 162
DSolve[y[x] (y'[x])^2+a x y'[x]+b y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} \text {Solve}\left [\frac {a \log \left (\sqrt {a^2-\frac {4 b y(x)^2}{x^2}}+a\right )+(a+2 b) \log \left (\sqrt {a^2-\frac {4 b y(x)^2}{x^2}}-a-2 b\right )}{4 (a+b)}=-\frac {\log (x)}{2}+c_1,y(x)\right ] \\ \text {Solve}\left [\frac {a \log \left (\sqrt {a^2-\frac {4 b y(x)^2}{x^2}}-a\right )+(a+2 b) \log \left (\sqrt {a^2-\frac {4 b y(x)^2}{x^2}}+a+2 b\right )}{4 (a+b)}=-\frac {\log (x)}{2}+c_1,y(x)\right ] \\ y(x)\to 0 \\ \end{align*}