53.1.4 problem 4

Internal problem ID [8438]
Book : Elementary differential equations. By Earl D. Rainville, Phillip E. Bedient. Macmilliam Publishing Co. NY. 6th edition. 1981.
Section : CHAPTER 16. Nonlinear equations. Section 94. Factoring the left member. EXERCISES Page 309
Problem number : 4
Date solved : Monday, January 27, 2025 at 04:00:42 PM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 19

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

\begin{align*} y &= c_{1} x \\ y &= \frac {-x +c_{1}}{x} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.044 (sec). Leaf size: 31

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

\begin{align*} y(x)\to c_1 x \\ y(x)\to -1+\frac {c_1}{x} \\ y(x)\to -1 \\ y(x)\to 0 \\ \end{align*}