62.7.2 problem Ex 2

Internal problem ID [12825]
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
Date solved : Tuesday, January 28, 2025 at 04:24:57 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.027 (sec). Leaf size: 33

dsolve(y(x)*diff(y(x),x)+x*y(x)^2=x,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: 1.933 (sec). Leaf size: 57

DSolve[y[x]*D[y[x],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*}