Internal problem ID [10602]
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: 7.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {\left (x +4\right ) \left (y^{2}+1\right )+y \left (x^{2}+3 x +2\right ) y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 122
dsolve((x+4)*(y(x)^2+1) + y(x)*(x^2+3*x+2)*diff(y(x),x)=0,y(x), singsol=all)
\begin{align*} y \left (x \right ) = \frac {\sqrt {-x^{6}+c_{1} x^{4}-6 x^{5}+8 c_{1} x^{3}+24 x^{2} c_{1} +100 x^{3}+32 x c_{1} +345 x^{2}+16 c_{1} +474 x +239}}{\left (x +1\right )^{3}} \\ y \left (x \right ) = -\frac {\sqrt {-x^{6}+c_{1} x^{4}-6 x^{5}+8 c_{1} x^{3}+24 x^{2} c_{1} +100 x^{3}+32 x c_{1} +345 x^{2}+16 c_{1} +474 x +239}}{\left (x +1\right )^{3}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 4.966 (sec). Leaf size: 126
DSolve[(x+4)*(y[x]^2+1) + y[x]*(x^2+3*x+2)*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {\sqrt {-(x+1)^6+e^{2 c_1} (x+2)^4}}{(x+1)^3} \\ y(x)\to \frac {\sqrt {-(x+1)^6+e^{2 c_1} (x+2)^4}}{(x+1)^3} \\ y(x)\to -i \\ y(x)\to i \\ y(x)\to \frac {(x+1)^3}{\sqrt {-(x+1)^6}} \\ y(x)\to \frac {\sqrt {-(x+1)^6}}{(x+1)^3} \\ \end{align*}