Internal problem ID [8054]
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]
Solve \begin {gather*} \boxed {2 y \left (y^{\prime }\right )^{2}-\left (4 x -5\right ) y^{\prime }+2 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.352 (sec). Leaf size: 131
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 \relax (x ) = x -\frac {5}{4} \\ y \relax (x ) = -x +\frac {5}{4} \\ y \relax (x ) = 0 \\ y \relax (x ) = \sqrt {16 c_{1}+2 \sqrt {-16 c_{1} x^{2}+40 c_{1} x -25 c_{1}}} \\ y \relax (x ) = \sqrt {16 c_{1}-2 \sqrt {-16 c_{1} x^{2}+40 c_{1} x -25 c_{1}}} \\ y \relax (x ) = -\sqrt {16 c_{1}+2 \sqrt {-16 c_{1} x^{2}+40 c_{1} x -25 c_{1}}} \\ y \relax (x ) = -\sqrt {16 c_{1}-2 \sqrt {-16 c_{1} x^{2}+40 c_{1} x -25 c_{1}}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.681 (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*}