Internal problem ID [6102]
Book: Elementary differential equations. By Earl D. Rainville, Phillip E. Bedient. Macmilliam
Publishing Co. NY. 6th edition. 1981.
Section: CHAPTER 16. Nonlinear equations. Section 101. Independent variable missing. EXERCISES
Page 324
Problem number: 38.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_xy]]
Solve \begin {gather*} \boxed {y^{\prime \prime }-2 x -\left (x^{2}-y^{\prime }\right )^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.078 (sec). Leaf size: 20
dsolve(diff(y(x),x$2)=2*x+(x^2-diff(y(x),x))^2,y(x), singsol=all)
\[ y \relax (x ) = \frac {x^{3}}{3}-\ln \left (c_{2} x -c_{1}\right ) \]
✓ Solution by Mathematica
Time used: 0.461 (sec). Leaf size: 24
DSolve[y''[x]==2*x+(x^2-y'[x])^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {x^3}{3}-\log (-x+c_1)+c_2 \\ \end{align*}