69.1.82 problem 127

Internal problem ID [14235]
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
Date solved : Tuesday, January 28, 2025 at 06:22:57 AM
CAS classification : [[_3rd_order, _missing_x], [_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2], [_3rd_order, _reducible, _mu_poly_yn]]

\begin{align*} y^{\prime \prime \prime }&={y^{\prime \prime }}^{2} \end{align*}

✓ Solution by Maple

Time used: 0.110 (sec). Leaf size: 24

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

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

✓ Solution by Mathematica

Time used: 0.342 (sec). Leaf size: 24

DSolve[D[y[x],{x,3}]==(D[y[x],{x,2}])^2,y[x],x,IncludeSingularSolutions -> True]
 

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