Internal problem ID [11149]
Book: An elementary treatise on differential equations by Abraham Cohen. DC heath publishers.
1906
Section: Chapter 2, differential equations of the first order and the first degree. Article 14.
Equations reducible to linear equations (Bernoulli). Page 21
Problem number: Ex 2.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {y y^{\prime }+y^{2} x=x} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 33
dsolve(y(x)*diff(y(x),x)+x*y(x)^2=x,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: 2.1 (sec). Leaf size: 57
DSolve[y[x]*y'[x]+x*y[x]^2==x,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*}