1.82 problem 127

Internal problem ID [12499]

Book: DIFFERENTIAL and INTEGRAL CALCULUS. VOL I. by N. PISKUNOV. MIR PUBLISHERS, Moscow 1969.
Section: Chapter 8. Differential equations. Exercises page 595
Problem number: 127.
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: 0.078 (sec). Leaf size: 24

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

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

✓ Solution by Mathematica

Time used: 0.607 (sec). Leaf size: 24

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

\[ y(x)\to x+c_3 x-(x+c_1) \log (x+c_1)+c_2 \]