53.4.33 problem 36

Internal problem ID [8521]
Book : Elementary differential equations. By Earl D. Rainville, Phillip E. Bedient. Macmilliam Publishing Co. NY. 6th edition. 1981.
Section : CHAPTER 16. Nonlinear equations. Section 101. Independent variable missing. EXERCISES Page 324
Problem number : 36
Date solved : Monday, January 27, 2025 at 04:09:12 PM
CAS classification : [[_2nd_order, _missing_y], _Liouville, [_2nd_order, _reducible, _mu_xy]]

\begin{align*} x y^{\prime \prime }&=y^{\prime } \left (2-3 x y^{\prime }\right ) \end{align*}

✓ Solution by Maple

Time used: 0.011 (sec). Leaf size: 16

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

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

✓ Solution by Mathematica

Time used: 0.293 (sec). Leaf size: 19

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

\[ y(x)\to \frac {1}{3} \log \left (x^3+c_1\right )+c_2 \]