53.4.2 problem 2

Internal problem ID [8490]
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 : 2
Date solved : Monday, January 27, 2025 at 04:07:18 PM
CAS classification : [[_2nd_order, _missing_y]]

\begin{align*} x^{2} y^{\prime \prime }+{y^{\prime }}^{2}-2 x y^{\prime }&=0 \end{align*}

With initial conditions

\begin{align*} y \left (2\right )&=5\\ y^{\prime }\left (2\right )&=-4 \end{align*}

✓ Solution by Maple

Time used: 0.074 (sec). Leaf size: 23

dsolve([x^2*diff(y(x),x$2)+diff(y(x),x)^2-2*x*diff(y(x),x)=0,y(2) = 5, D(y)(2) = -4],y(x), singsol=all)
 

\[ y = \frac {x^{2}}{2}+3 x +9 \ln \left (x -3\right )-3-9 i \pi \]

✓ Solution by Mathematica

Time used: 0.464 (sec). Leaf size: 28

DSolve[{x^2*D[y[x],{x,2}]+(D[y[x],x])^2-2*x*D[y[x],x]==0,{y[2]==5,Derivative[1][y][2]==-4}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {x^2}{2}+3 x+9 \log (x-3)-9 i \pi -3 \]