Internal problem ID [4247]
Book: Mathematical Methods in the Physical Sciences. third edition. Mary L. Boas. John Wiley.
2006
Section: Chapter 8, Ordinary differential equations. Section 2. Separable equations. page
398
Problem number: 7.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y y^{\prime }+y^{2} x -8 x=0} \end {gather*} With initial conditions \begin {align*} [y \relax (1) = 3] \end {align*}
✓ Solution by Maple
Time used: 0.059 (sec). Leaf size: 17
dsolve([y(x)*diff(y(x),x)+(x*y(x)^2-8*x)=0,y(1) = 3],y(x), singsol=all)
\[ y \relax (x ) = \sqrt {{\mathrm e}^{-\left (x -1\right ) \left (x +1\right )}+8} \]
✓ Solution by Mathematica
Time used: 0.306 (sec). Leaf size: 39
DSolve[{y[x]*y'[x]+(x*y[x]^2-8*x)==0,{y[1]==3}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \sqrt {e^{1-x^2}+8} \\ y(x)\to \sqrt {e^{1-x^2}+8} \\ \end{align*}