Internal problem ID [5289]
Book: Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres.
McGraw Hill 1952
Section: Chapter 5. Equations of first order and first degree (Exact equations). Supplemetary
problems. Page 33
Problem number: 26 (b).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {y^{2}-\left (x^{2}+x \right ) y^{\prime }=-1} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 15
dsolve(1+y(x)^2=(x+x^2)*diff(y(x),x),y(x), singsol=all)
\[ y \left (x \right ) = \tan \left (-\ln \left (x +1\right )+\ln \left (x \right )+c_{1} \right ) \]
✓ Solution by Mathematica
Time used: 0.228 (sec). Leaf size: 31
DSolve[1+y[x]^2==(x+x^2)*y'[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \tan (\log (x)-\log (x+1)+c_1) \\ y(x)\to -i \\ y(x)\to i \\ \end{align*}