40.4.11 problem 19 (L)

Internal problem ID [6651]
Book : Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres. McGraw Hill 1952
Section : Chapter 6. Equations of first order and first degree (Linear equations). Supplemetary problems. Page 39
Problem number : 19 (L)
Date solved : Monday, January 27, 2025 at 02:16:57 PM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 29

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

\begin{align*} y &= \sqrt {{\mathrm e}^{x^{2}} c_1 +1} \\ y &= -\sqrt {{\mathrm e}^{x^{2}} c_1 +1} \\ \end{align*}

✓ Solution by Mathematica

Time used: 1.873 (sec). Leaf size: 53

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

\begin{align*} y(x)\to -\sqrt {1+e^{x^2+2 c_1}} \\ y(x)\to \sqrt {1+e^{x^2+2 c_1}} \\ y(x)\to -1 \\ y(x)\to 1 \\ \end{align*}