53.4.25 problem 27

Internal problem ID [8513]
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 : 27
Date solved : Monday, January 27, 2025 at 04:08:41 PM
CAS classification : [[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]]

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

✓ Solution by Maple

Time used: 0.019 (sec). Leaf size: 21

dsolve(x^2*diff(y(x),x$2)+diff(y(x),x)^2=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.569 (sec). Leaf size: 47

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

\begin{align*} y(x)\to -\frac {x}{c_1}+\frac {\log (1+c_1 x)}{c_1{}^2}+c_2 \\ y(x)\to c_2 \\ y(x)\to -\frac {x^2}{2}+c_2 \\ \end{align*}