77.1.99 problem 126 (page 179)

Internal problem ID [17989]
Book : V.V. Stepanov, A course of differential equations (in Russian), GIFML. Moscow (1958)
Section : All content
Problem number : 126 (page 179)
Date solved : Tuesday, January 28, 2025 at 11:19:30 AM
CAS classification : [[_high_order, _missing_x], [_high_order, _missing_y], [_high_order, _with_linear_symmetries], [_high_order, _reducible, _mu_poly_yn]]

\begin{align*} 5 {y^{\prime \prime \prime }}^{2}-3 y^{\prime \prime } y^{\prime \prime \prime \prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.110 (sec). Leaf size: 36

dsolve(5*diff(y(x),x$3)^2-3*diff(y(x),x$2)*diff(y(x),x$4)=0,y(x), singsol=all)
 

\begin{align*} y &= c_{1} x +c_{2} \\ y &= 3 \left (x +c_{2} \right ) \sqrt {6}\, c_{1} \sqrt {-\frac {c_{1}}{x +c_{2}}}+c_{3} x +c_4 \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.206 (sec). Leaf size: 28

DSolve[5*D[y[x],{x,3}]^2-3*D[y[x],{x,2}]*D[y[x],{x,4}]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to c_2 \left (-\sqrt {2 x+3 c_1}\right )+c_4 x+c_3 \]