78.7.4 problem 1 (d)

Internal problem ID [18190]
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. Section 11 (Reduction of order). Problems at page 87
Problem number : 1 (d)
Date solved : Tuesday, January 28, 2025 at 11:37:39 AM
CAS classification : [[_2nd_order, _missing_y]]

\begin{align*} x^{2} y^{\prime \prime }&=2 x y^{\prime }+{y^{\prime }}^{2} \end{align*}

✓ Solution by Maple

Time used: 0.011 (sec). Leaf size: 26

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

\[ y = -c_1 x -\frac {x^{2}}{2}-c_1^{2} \ln \left (-c_1 +x \right )+c_2 \]

✓ Solution by Mathematica

Time used: 0.400 (sec). Leaf size: 41

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

\[ y(x)\to -\frac {x^2}{2}-c_1 x-c_1{}^2 \log (x-c_1)+\frac {3 c_1{}^2}{2}+c_2 \]