50.7.4 problem 1(d)

Internal problem ID [7908]
Book : Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz. McGraw-Hill NY. 2007. 1st Edition.
Section : Chapter 1. What is a differential equation. Section 1.9. Reduction of Order. Page 38
Problem number : 1(d)
Date solved : Monday, January 27, 2025 at 03:31:51 PM
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: 0.040 (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)
 

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

✓ Solution by Mathematica

Time used: 0.471 (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]
 

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