73.3.19 problem 4.5 (c)

Internal problem ID [15053]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 4. SEPARABLE FIRST ORDER EQUATIONS. Additional exercises. page 90
Problem number : 4.5 (c)
Date solved : Tuesday, January 28, 2025 at 07:28:51 AM
CAS classification : [_separable]

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

With initial conditions

\begin{align*} y \left (0\right )&=-2 \end{align*}

✓ Solution by Maple

Time used: 0.097 (sec). Leaf size: 16

dsolve([y(x)*diff(y(x),x)=x*y(x)^2+x,y(0) = -2],y(x), singsol=all)
 

\[ y = -\sqrt {5 \,{\mathrm e}^{x^{2}}-1} \]

✓ Solution by Mathematica

Time used: 6.997 (sec). Leaf size: 20

DSolve[{y[x]*D[y[x],x]==x*y[x]^2+x,{y[0]==-2}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -\sqrt {5 e^{x^2}-1} \]