Internal problem ID [5308]
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).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {y^{\prime } y-x y^{2}=-x} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 29
dsolve(y(x)*diff(y(x),x)-x*y(x)^2+x=0,y(x), singsol=all)
\begin{align*} y \left (x \right ) &= \sqrt {{\mathrm e}^{x^{2}} c_{1} +1} \\ y \left (x \right ) &= -\sqrt {{\mathrm e}^{x^{2}} c_{1} +1} \\ \end{align*}
✓ Solution by Mathematica
Time used: 1.859 (sec). Leaf size: 53
DSolve[y[x]*y'[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*}