78.8.35 problem 35

Internal problem ID [18233]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 2. First order equations. Miscellaneous Problems for Chapter 2. Problems at page 99
Problem number : 35
Date solved : Tuesday, January 28, 2025 at 11:42:58 AM
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: 0.011 (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: 0.372 (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]
 

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