Internal problem ID [12971]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 3. Some basics about First order equations. Additional exercises. page
63
Problem number: 3.4 d.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {y^{\prime } x^{2}+x y^{2}=x} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 9
dsolve(x^2*diff(y(x),x)+x*y(x)^2=x,y(x), singsol=all)
\[ y = \tanh \left (\ln \left (x \right )+c_{1} \right ) \]
✓ Solution by Mathematica
Time used: 1.054 (sec). Leaf size: 40
DSolve[x^2*y'[x]+x*y[x]^2==x,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {x^2-e^{2 c_1}}{x^2+e^{2 c_1}} y(x)\to -1 y(x)\to 1 \end{align*}