53.4.32 problem 35

Internal problem ID [8520]
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 : 35
Date solved : Monday, January 27, 2025 at 04:09:11 PM
CAS classification : [[_2nd_order, _missing_y]]

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

✓ Solution by Maple

Time used: 0.021 (sec). Leaf size: 22

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

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

✓ Solution by Mathematica

Time used: 0.353 (sec). Leaf size: 28

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

\[ y(x)\to \frac {1}{2} \left (x^2-c_1 \log \left (x^2+c_1\right )+2 c_2\right ) \]