Internal problem ID [5228]
Book: Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres.
McGraw Hill 1952
Section: Chapter 2. Solutions of differential equations. Supplemetary problems. Page
11
Problem number: 15.
ODE order: 1.
ODE degree: 4.
CAS Maple gives this as type [[_1st_order, _with_linear_symmetries], _Clairaut]
\[ \boxed {y-x y^{\prime }-{y^{\prime }}^{4}=0} \]
✓ Solution by Maple
Time used: 0.078 (sec). Leaf size: 66
dsolve(y(x)=x*diff(y(x),x)+diff(y(x),x)^4,y(x), singsol=all)
\begin{align*} y \left (x \right ) &= -\frac {3 \,2^{\frac {1}{3}} \left (-x \right )^{\frac {4}{3}}}{8} \\ y \left (x \right ) &= \frac {3 \,2^{\frac {1}{3}} \left (-x \right )^{\frac {4}{3}} \left (1+i \sqrt {3}\right )}{16} \\ y \left (x \right ) &= -\frac {3 \,2^{\frac {1}{3}} \left (-x \right )^{\frac {4}{3}} \left (i \sqrt {3}-1\right )}{16} \\ y \left (x \right ) &= c_{1} \left (c_{1}^{3}+x \right ) \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.007 (sec). Leaf size: 75
DSolve[y[x]==x*y'[x]+(y'[x])^4,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 \left (x+c_1{}^3\right ) \\ y(x)\to -\frac {3}{4} \left (-\frac {1}{2}\right )^{2/3} x^{4/3} \\ y(x)\to -\frac {3 x^{4/3}}{4\ 2^{2/3}} \\ y(x)\to \frac {3 \sqrt [3]{-1} x^{4/3}}{4\ 2^{2/3}} \\ \end{align*}