Internal problem ID [8126]
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]
Solve \begin {gather*} \boxed {\left (y^{\prime }\right )^{4}+3 \left (x -1\right ) \left (y^{\prime }\right )^{2}-3 \left (2 y-1\right ) y^{\prime }+3 x=0} \end {gather*}
✓ Solution by Maple
Time used: 0.078 (sec). Leaf size: 245
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 \relax (x ) = \frac {1}{6}+x \\ y \relax (x ) = \frac {5}{6}-x \\ y \relax (x ) = \frac {\left (3 \left (-\frac {c_{1}}{2}-\frac {\sqrt {c_{1}^{2}+4 x}}{2}\right )^{2}+3\right ) x}{-3 c_{1}-3 \sqrt {c_{1}^{2}+4 x}}+\frac {\left (-\frac {c_{1}}{2}-\frac {\sqrt {c_{1}^{2}+4 x}}{2}\right )^{4}-3 \left (-\frac {c_{1}}{2}-\frac {\sqrt {c_{1}^{2}+4 x}}{2}\right )^{2}-\frac {3 c_{1}}{2}-\frac {3 \sqrt {c_{1}^{2}+4 x}}{2}}{-3 c_{1}-3 \sqrt {c_{1}^{2}+4 x}} \\ y \relax (x ) = \frac {\left (3 \left (-\frac {c_{1}}{2}+\frac {\sqrt {c_{1}^{2}+4 x}}{2}\right )^{2}+3\right ) x}{-3 c_{1}+3 \sqrt {c_{1}^{2}+4 x}}+\frac {\left (-\frac {c_{1}}{2}+\frac {\sqrt {c_{1}^{2}+4 x}}{2}\right )^{4}-3 \left (-\frac {c_{1}}{2}+\frac {\sqrt {c_{1}^{2}+4 x}}{2}\right )^{2}-\frac {3 c_{1}}{2}+\frac {3 \sqrt {c_{1}^{2}+4 x}}{2}}{-3 c_{1}+3 \sqrt {c_{1}^{2}+4 x}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.49 (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 (-c_1 \left (6 x-6+c_1{}^2\right )-\sqrt {\left (4 x+c_1{}^2\right ){}^3}+6\right ) \\ y(x)\to \frac {1}{12} \left (-c_1 \left (6 x-6+c_1{}^2\right )+\sqrt {\left (4 x+c_1{}^2\right ){}^3}+6\right ) \\ \end{align*}