15.1.30 problem 30

Internal problem ID [2870]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 5, page 21
Problem number : 30
Date solved : Monday, January 27, 2025 at 06:21:13 AM
CAS classification : [_separable]

\begin{align*} \left (x^{2}-2 x -8\right ) y^{\prime }&=y^{2}+y-2 \end{align*}

With initial conditions

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

✓ Solution by Maple

Time used: 0.208 (sec). Leaf size: 31

dsolve([(x^2-2*x-8)*diff(y(x),x)=y(x)^2+y(x)-2,y(0) = 0],y(x), singsol=all)
 

\[ y = \frac {2 x +8-2 \sqrt {-2 x^{2}+4 x +16}}{3 x +4} \]

✓ Solution by Mathematica

Time used: 3.823 (sec). Leaf size: 48

DSolve[{(x^2-2*x-8)*D[y[x],x]==y[x]^2+y[x]-2,y[0]==0},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {4 \sqrt {x+2}-2 \sqrt {8-2 x}}{\sqrt {8-2 x}+4 \sqrt {x+2}} \]