Internal problem ID [940]
Book: Elementary differential equations with boundary value problems. William F. Trench.
Brooks/Cole 2001
Section: Chapter 2, First order equations. separable equations. Section 2.2 Page 52
Problem number: 14.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{\prime }+\frac {\left (1+y\right ) \left (y-1\right ) \left (y-2\right )}{x +1}=0} \end {gather*} With initial conditions \begin {align*} [y \relax (1) = 0] \end {align*}
✓ Solution by Maple
Time used: 1.578 (sec). Leaf size: 111
dsolve([diff(y(x),x)+((y(x)+1)*(y(x)-1)*(y(x)-2))/(x+1)=0,y(1) = 0],y(x), singsol=all)
\[ y \relax (x ) = \RootOf \left (-2048+\left (x^{6}+6 x^{5}+15 x^{4}+20 x^{3}+15 x^{2}+6 x +257\right ) \textit {\_Z}^{18}+\left (-6 x^{6}-36 x^{5}-90 x^{4}-120 x^{3}-90 x^{2}-36 x -1542\right ) \textit {\_Z}^{12}+\left (9 x^{6}+54 x^{5}+135 x^{4}+180 x^{3}+135 x^{2}+54 x +3081\right ) \textit {\_Z}^{6}\right )^{6}-1 \]
✓ Solution by Mathematica
Time used: 60.946 (sec). Leaf size: 1128
DSolve[{y'[x]+((y[x]+1)*(y[x]-1)*(y[x]-2))/(x+1)==0,y[1]==0},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {\left (-1-i \sqrt {3}\right ) x^{12}-12 i \left (-i+\sqrt {3}\right ) x^{11}-66 i \left (-i+\sqrt {3}\right ) x^{10}-220 i \left (-i+\sqrt {3}\right ) x^9-495 i \left (-i+\sqrt {3}\right ) x^8-792 i \left (-i+\sqrt {3}\right ) x^7+2 \left (\sqrt [3]{-x (x+2) \left (x^2+x+1\right ) (x (x+3)+3) \left (x (x (x+3)+3) (x+1)^3+257\right ) (x (x (x+3)+3) (x (x (x+3)+3)+3)+259)+16 \sqrt {(x+1)^{12} \left (x (x+2) \left (x^2+x+1\right ) (x (x+3)+3)+257\right )^3}-66049}-590 i \sqrt {3}-590\right ) x^6+12 \left (\sqrt [3]{-x (x+2) \left (x^2+x+1\right ) (x (x+3)+3) \left (x (x (x+3)+3) (x+1)^3+257\right ) (x (x (x+3)+3) (x (x (x+3)+3)+3)+259)+16 \sqrt {(x+1)^{12} \left (x (x+2) \left (x^2+x+1\right ) (x (x+3)+3)+257\right )^3}-66049}-194 i \sqrt {3}-194\right ) x^5+15 \left (2 \sqrt [3]{-x (x+2) \left (x^2+x+1\right ) (x (x+3)+3) \left (x (x (x+3)+3) (x+1)^3+257\right ) (x (x (x+3)+3) (x (x (x+3)+3)+3)+259)+16 \sqrt {(x+1)^{12} \left (x (x+2) \left (x^2+x+1\right ) (x (x+3)+3)+257\right )^3}-66049}-289 i \sqrt {3}-289\right ) x^4+20 \left (2 \sqrt [3]{-x (x+2) \left (x^2+x+1\right ) (x (x+3)+3) \left (x (x (x+3)+3) (x+1)^3+257\right ) (x (x (x+3)+3) (x (x (x+3)+3)+3)+259)+16 \sqrt {(x+1)^{12} \left (x (x+2) \left (x^2+x+1\right ) (x (x+3)+3)+257\right )^3}-66049}-267 i \sqrt {3}-267\right ) x^3+6 \left (5 \sqrt [3]{-x (x+2) \left (x^2+x+1\right ) (x (x+3)+3) \left (x (x (x+3)+3) (x+1)^3+257\right ) (x (x (x+3)+3) (x (x (x+3)+3)+3)+259)+16 \sqrt {(x+1)^{12} \left (x (x+2) \left (x^2+x+1\right ) (x (x+3)+3)+257\right )^3}-66049}-651 i \sqrt {3}-651\right ) x^2+12 \left (\sqrt [3]{-x (x+2) \left (x^2+x+1\right ) (x (x+3)+3) \left (x (x (x+3)+3) (x+1)^3+257\right ) (x (x (x+3)+3) (x (x (x+3)+3)+3)+259)+16 \sqrt {(x+1)^{12} \left (x (x+2) \left (x^2+x+1\right ) (x (x+3)+3)+257\right )^3}-66049}-129 i \sqrt {3}-129\right ) x+257 \left (2 \sqrt [3]{-x (x+2) \left (x^2+x+1\right ) (x (x+3)+3) \left (x (x (x+3)+3) (x+1)^3+257\right ) (x (x (x+3)+3) (x (x (x+3)+3)+3)+259)+16 \sqrt {(x+1)^{12} \left (x (x+2) \left (x^2+x+1\right ) (x (x+3)+3)+257\right )^3}-66049}-i \sqrt {3}-1\right )+i \left (i+\sqrt {3}\right ) \left (-x (x+2) \left (x^2+x+1\right ) (x (x+3)+3) \left (x (x (x+3)+3) (x+1)^3+257\right ) (x (x (x+3)+3) (x (x (x+3)+3)+3)+259)+16 \sqrt {(x+1)^{12} \left (x (x+2) \left (x^2+x+1\right ) (x (x+3)+3)+257\right )^3}-66049\right )^{2/3}}{2 \left (x (x+2) \left (x^2+x+1\right ) (x (x+3)+3)+257\right ) \sqrt [3]{-x (x+2) \left (x^2+x+1\right ) (x (x+3)+3) \left (x (x (x+3)+3) (x+1)^3+257\right ) (x (x (x+3)+3) (x (x (x+3)+3)+3)+259)+16 \sqrt {(x+1)^{12} \left (x (x+2) \left (x^2+x+1\right ) (x (x+3)+3)+257\right )^3}-66049}} \\ \end{align*}