Internal problem ID [7744]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 164.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational, _Riccati]
Solve \begin {gather*} \boxed {2 x^{2} y^{\prime }-2 y^{2}-3 y x +2 a^{2} x=0} \end {gather*}
✓ Solution by Maple
Time used: 0.024 (sec). Leaf size: 102
dsolve(2*x^2*diff(y(x),x) - 2*y(x)^2 - 3*x*y(x) + 2*a^2*x=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {\left (-2 \sqrt {-\frac {a^{2}}{x}}\, x c_{1}-x \right ) \sin \left (2 \sqrt {-\frac {a^{2}}{x}}\right )-x \left (c_{1}-2 \sqrt {-\frac {a^{2}}{x}}\right ) \cos \left (2 \sqrt {-\frac {a^{2}}{x}}\right )}{2 \cos \left (2 \sqrt {-\frac {a^{2}}{x}}\right ) c_{1}+2 \sin \left (2 \sqrt {-\frac {a^{2}}{x}}\right )} \]
✓ Solution by Mathematica
Time used: 0.261 (sec). Leaf size: 66
DSolve[2*x^2*y'[x]- 2*y[x]^2 - 3*x*y[x] + 2*a^2*x==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {4 a^2 c_1 \sqrt {x}}{e^{\frac {4 a}{\sqrt {x}}}-2 a c_1}+a \sqrt {x}-\frac {x}{2} \\ y(x)\to a \left (-\sqrt {x}\right )-\frac {x}{2} \\ \end{align*}