53.1.5 problem 5

Internal problem ID [8439]
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 : 5
Date solved : Monday, January 27, 2025 at 04:00:46 PM
CAS classification : [_quadrature]

\begin{align*} x {y^{\prime }}^{2}+\left (1-x^{2} y\right ) y^{\prime }-y x&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 21

dsolve(x*diff(y(x),x)^2+(1-x^2*y(x))*diff(y(x),x)-x*y(x)=0,y(x), singsol=all)
 

\begin{align*} y &= -\ln \left (x \right )+c_{1} \\ y &= {\mathrm e}^{\frac {x^{2}}{2}} c_{1} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.011 (sec). Leaf size: 28

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

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