Internal problem ID [8809]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 474.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [[_homogeneous, `class C`], _rational, _dAlembert]
\[ \boxed {2 y {y^{\prime }}^{2}-\left (4 x -5\right ) y^{\prime }+2 y=0} \]
✓ Solution by Maple
Time used: 0.125 (sec). Leaf size: 135
dsolve(2*y(x)*diff(y(x),x)^2-(4*x-5)*diff(y(x),x)+2*y(x) = 0,y(x), singsol=all)
\begin{align*} y \left (x \right ) = x -\frac {5}{4} y \left (x \right ) = -x +\frac {5}{4} y \left (x \right ) = 0 y \left (x \right ) = \frac {\sqrt {4 c_{1} +2 \sqrt {-16 x^{2} c_{1} +40 x c_{1} -25 c_{1}}}}{2} y \left (x \right ) = -\frac {\sqrt {4 c_{1} +2 \sqrt {-16 x^{2} c_{1} +40 x c_{1} -25 c_{1}}}}{2} y \left (x \right ) = \frac {\sqrt {4 c_{1} -2 \sqrt {-16 x^{2} c_{1} +40 x c_{1} -25 c_{1}}}}{2} y \left (x \right ) = -\frac {\sqrt {4 c_{1} -2 \sqrt {-16 x^{2} c_{1} +40 x c_{1} -25 c_{1}}}}{2} \end{align*}
✓ Solution by Mathematica
Time used: 0.659 (sec). Leaf size: 160
DSolve[2*y[x] - (-5 + 4*x)*y'[x] + 2*y[x]*y'[x]^2==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -i \sqrt {2} e^{\frac {c_1}{2}} \sqrt {4 x-5+8 e^{c_1}} y(x)\to i \sqrt {2} e^{\frac {c_1}{2}} \sqrt {4 x-5+8 e^{c_1}} y(x)\to -\frac {1}{4} i e^{\frac {c_1}{2}} \sqrt {8 x-10+e^{c_1}} y(x)\to \frac {1}{4} i e^{\frac {c_1}{2}} \sqrt {8 x-10+e^{c_1}} y(x)\to 0 y(x)\to \frac {5}{4}-x y(x)\to x-\frac {5}{4} \end{align*}