1.83 problem 128

Internal problem ID [12500]

Book: DIFFERENTIAL and INTEGRAL CALCULUS. VOL I. by N. PISKUNOV. MIR PUBLISHERS, Moscow 1969.
Section: Chapter 8. Differential equations. Exercises page 595
Problem number: 128.
ODE order: 2.
ODE degree: 1.

CAS Maple gives this as type [[_3rd_order, _missing_x], [_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2], [_3rd_order, _reducible, _mu_poly_yn]]

✓ Solution by Maple

Time used: 0.156 (sec). Leaf size: 59

dsolve(diff(y(x),x)*diff(y(x),x$3)-3*diff(y(x),x$2)^2=0,y(x), singsol=all)
 

\begin{align*} y \left (x \right ) &= c_{1} \\ y \left (x \right ) &= \frac {-c_{1} c_{2} +\sqrt {-2 \left (-\frac {c_{1} c_{2}^{2}}{2}+x +c_{3} \right ) c_{1}}}{c_{1}} \\ y \left (x \right ) &= \frac {-c_{1} c_{2} -\sqrt {-2 \left (-\frac {c_{1} c_{2}^{2}}{2}+x +c_{3} \right ) c_{1}}}{c_{1}} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.307 (sec). Leaf size: 21

DSolve[y'[x]*y'''[x]-3*(y''[x])^2==0,y[x],x,IncludeSingularSolutions -> True]
                                                                                    
                                                                                    
 

\[ y(x)\to c_2 \sqrt {2 x+c_1}+c_3 \]