83.32.3 problem 3

Internal problem ID [19402]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter VII. Exact differential equations and certain particular forms of equations. Exercise VII (F) at page 113
Problem number : 3
Date solved : Tuesday, January 28, 2025 at 01:37:56 PM
CAS classification : [[_3rd_order, _missing_x], [_3rd_order, _missing_y], [_3rd_order, _exact, _nonlinear], [_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: 0.058 (sec). Leaf size: 31

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

\begin{align*} y \left (x \right ) &= -\frac {8 \left (x +c_{1} \right )^{{5}/{2}}}{15}+c_{2} x +c_3 \\ y \left (x \right ) &= \frac {8 \left (x +c_{1} \right )^{{5}/{2}}}{15}+c_{2} x +c_3 \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.174 (sec). Leaf size: 61

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

\begin{align*} y(x)\to -\frac {1}{15} \sqrt {2} (2 x+c_1){}^{5/2}+c_3 x+c_2 \\ y(x)\to \frac {1}{15} \sqrt {2} (2 x+c_1){}^{5/2}+c_3 x+c_2 \\ \end{align*}