60.1.543 problem 546

Internal problem ID [10557]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 546
Date solved : Monday, January 27, 2025 at 09:04:35 PM
CAS classification : [_dAlembert]

\begin{align*} {y^{\prime }}^{4}+3 \left (x -1\right ) {y^{\prime }}^{2}-3 \left (2 y-1\right ) y^{\prime }+3 x&=0 \end{align*}

✓ Solution by Maple

Time used: 0.089 (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 &= x +\frac {1}{6} \\ y &= \frac {5}{6}-x \\ y &= \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 &= \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 \sqrt {c_{1}^{2}+4 x}+6 c_{1}} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.446 (sec). Leaf size: 77

DSolve[3*x - 3*(-1 + 2*y[x])*D[y[x],x] + 3*(-1 + x)*D[y[x],x]^2 + D[y[x],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*}