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]
\[ \boxed {y-y^{\prime } x -{y^{\prime }}^{4}=0} \]
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 19
dsolve(y(x)=x*diff(y(x),x)+diff(y(x),x)^4,y(x), singsol=all)
\begin{align*} y = c_{1}^{4}+c_{1} x y = c_{1} x^{\frac {4}{3}} \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*}