Internal problem ID [11640]
Book: Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi.
2004.
Section: Chapter 2, section 2.2 (Separable equations). Exercises page 47
Problem number: 17.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {\left (3 x +8\right ) \left (y^{2}+4\right )-4 y \left (x^{2}+5 x +6\right ) y^{\prime }=0} \] With initial conditions \begin {align*} [y \left (1\right ) = 2] \end {align*}
✓ Solution by Maple
Time used: 0.062 (sec). Leaf size: 21
dsolve([(3*x+8)*(y(x)^2+4)-4*y(x)*(x^2+5*x+6)*diff(y(x),x)=0,y(1) = 2],y(x), singsol=all)
\[ y \left (x \right ) = \frac {2 \sqrt {-9+\left (3 x +6\right ) \sqrt {3+x}}}{3} \]
✓ Solution by Mathematica
Time used: 4.88 (sec). Leaf size: 36
DSolve[{(3*x+8)*(y[x]^2+4)-4*y[x]*(x^2+5*x+6)*y'[x]==0,{y[1]==2}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {2 \sqrt {\sqrt {x+3} x+2 \sqrt {x+3}-3}}{\sqrt {3}} \]