53.4.35 problem 38

Internal problem ID [8523]
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
Date solved : Monday, January 27, 2025 at 04:09:14 PM
CAS classification : [[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_xy]]

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

✓ Solution by Maple

Time used: 0.010 (sec). Leaf size: 20

dsolve(diff(y(x),x$2)=2*x+(x^2-diff(y(x),x))^2,y(x), singsol=all)
 

\[ y = \frac {x^{3}}{3}-\ln \left (c_{2} x -c_{1} \right ) \]

✓ Solution by Mathematica

Time used: 0.316 (sec). Leaf size: 24

DSolve[D[y[x],{x,2}]==2*x+(x^2-D[y[x],x])^2,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {x^3}{3}-\log (-x+c_1)+c_2 \]