Internal problem ID [8053]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 473.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [[_homogeneous, class C], _dAlembert]
Solve \begin {gather*} \boxed {\left (y-2 x \right ) \left (y^{\prime }\right )^{2}-2 \left (x -1\right ) y^{\prime }+y-2=0} \end {gather*}
✓ Solution by Maple
Time used: 8.046 (sec). Leaf size: 587
dsolve((y(x)-2*x)*diff(y(x),x)^2-2*(x-1)*diff(y(x),x)+y(x)-2 = 0,y(x), singsol=all)
\begin{align*} y \relax (x ) = 2+\frac {c_{1}}{2}-\frac {\sqrt {-c_{1}^{2}+4 c_{1} \left (x -1\right )}}{2} \\ y \relax (x ) = 2+c_{1}-\sqrt {-c_{1}^{2}+2 c_{1} \left (x -1\right )} \\ \text {Expression too large to display} \\ \end{align*}
✓ Solution by Mathematica
Time used: 4.544 (sec). Leaf size: 187
DSolve[-2 + y[x] - 2*(-1 + x)*y'[x] + (-2*x + y[x])*y'[x]^2==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {1}{2} \sqrt {-e^{c_1} \left (4 x-4+e^{c_1}\right )}+2-\frac {e^{c_1}}{2} \\ y(x)\to \frac {1}{2} \left (\sqrt {-e^{c_1} \left (4 x-4+e^{c_1}\right )}+4-e^{c_1}\right ) \\ y(x)\to -\sqrt {-e^{c_1} \left (2 x-2+e^{c_1}\right )}+2-e^{c_1} \\ y(x)\to \sqrt {-e^{c_1} \left (2 x-2+e^{c_1}\right )}+2-e^{c_1} \\ y(x)\to 2 \\ y(x)\to x-\sqrt {2} \sqrt {(x-1)^2}+1 \\ y(x)\to x+\sqrt {2} \sqrt {(x-1)^2}+1 \\ \end{align*}