35.2.7 problem 7

Internal problem ID [6099]
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
Date solved : Monday, January 27, 2025 at 01:36:05 PM
CAS classification : [_separable]

\begin{align*} y^{\prime } y+x y^{2}-8 x&=0 \end{align*}

With initial conditions

\begin{align*} y \left (1\right )&=3 \end{align*}

✓ Solution by Maple

Time used: 0.056 (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)
 

\[ y = \sqrt {{\mathrm e}^{-\left (x -1\right ) \left (x +1\right )}+8} \]

✓ Solution by Mathematica

Time used: 1.938 (sec). Leaf size: 39

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