Internal problem ID [12997]
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).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {y y^{\prime }-x y^{2}=x} \] With initial conditions \begin {align*} [y \left (0\right ) = -2] \end {align*}
✓ Solution by Maple
Time used: 0.015 (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: 7.0 (sec). Leaf size: 20
DSolve[{y[x]*y'[x]==x*y[x]^2+x,{y[0]==-2}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -\sqrt {5 e^{x^2}-1} \]