Internal problem ID [8881]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 546.
ODE order: 1.
ODE degree: 4.
CAS Maple gives this as type [_dAlembert]
\[ \boxed {{y^{\prime }}^{4}+3 \left (x -1\right ) {y^{\prime }}^{2}-3 \left (2 y-1\right ) y^{\prime }=-3 x} \]
✓ Solution by Maple
Time used: 0.078 (sec). Leaf size: 149
dsolve(diff(y(x),x)^4+3*(x-1)*diff(y(x),x)^2-3*(2*y(x)-1)*diff(y(x),x)+3*x=0,y(x), singsol=all)
\begin{align*} y \left (x \right ) &= x +\frac {1}{6} \\ y \left (x \right ) &= -x +\frac {5}{6} \\ y \left (x \right ) &= \frac {\left (3-c_{1}^{3}+\left (-5 x +3\right ) c_{1} \right ) \sqrt {c_{1}^{2}+4 x}-c_{1}^{4}+\left (-7 x +3\right ) c_{1}^{2}+3 c_{1} -8 x^{2}}{6 c_{1} +6 \sqrt {c_{1}^{2}+4 x}} \\ y \left (x \right ) &= \frac {\left (-3+c_{1}^{3}+\left (5 x -3\right ) c_{1} \right ) \sqrt {c_{1}^{2}+4 x}-c_{1}^{4}+\left (-7 x +3\right ) c_{1}^{2}+3 c_{1} -8 x^{2}}{6 c_{1} -6 \sqrt {c_{1}^{2}+4 x}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.496 (sec). Leaf size: 77
DSolve[3*x - 3*(-1 + 2*y[x])*y'[x] + 3*(-1 + x)*y'[x]^2 + y'[x]^4==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{12} \left (-6 c_1 (x-1)-\sqrt {\left (4 x+c_1{}^2\right ){}^3}+6-c_1{}^3\right ) \\ y(x)\to \frac {1}{12} \left (-6 c_1 (x-1)+\sqrt {\left (4 x+c_1{}^2\right ){}^3}+6-c_1{}^3\right ) \\ \end{align*}