Internal problem ID [7867]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 287.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class C], _rational, _dAlembert]
Solve \begin {gather*} \boxed {\left (2 y-4 x +1\right )^{2} y^{\prime }-\left (y-2 x \right )^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.075 (sec). Leaf size: 56
dsolve((2*y(x)-4*x+1)^2*diff(y(x),x)-(y(x)-2*x)^2=0,y(x), singsol=all)
\[ -\frac {x}{7}-\frac {9 \sqrt {2}\, \arctanh \left (\frac {\left (14 y \relax (x )-28 x +8\right ) \sqrt {2}}{4}\right )}{98}-\frac {2 \ln \left (7 \left (y \relax (x )-2 x \right )^{2}+8 y \relax (x )-16 x +2\right )}{49}+\frac {4 y \relax (x )}{7}-c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 1.794 (sec). Leaf size: 77
DSolve[(2*y[x]-4*x+1)^2*y'[x]-(y[x]-2*x)^2==0,y[x],x,IncludeSingularSolutions -> True]
\[ \operatorname {Solve}\left [\frac {y(x)}{2}+\frac {1}{196} \left (14 y(x)-\left (8-9 \sqrt {2}\right ) \log \left (-7 y(x)+14 x+\sqrt {2}-4\right )-\left (8+9 \sqrt {2}\right ) \log \left (7 y(x)-14 x+\sqrt {2}+4\right )-28 x\right )=c_1,y(x)\right ] \]