Internal problem ID [944]
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: 18.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{\prime }+2 x \left (y^{3}-3 y+2\right )=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 3] \end {align*}
✓ Solution by Maple
Time used: 0.344 (sec). Leaf size: 70
dsolve([diff(y(x),x)=-2*x*(y(x)^3-3*y(x)+2),y(0) = 3],y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{\RootOf \left (18 x^{2} {\mathrm e}^{\textit {\_Z}}-2 \ln \left ({\mathrm e}^{\textit {\_Z}}-3\right ) {\mathrm e}^{\textit {\_Z}}+2 \,{\mathrm e}^{\textit {\_Z}} \ln \relax (2)-2 \,{\mathrm e}^{\textit {\_Z}} \ln \relax (5)+2 \textit {\_Z} \,{\mathrm e}^{\textit {\_Z}}-54 x^{2}+3 \,{\mathrm e}^{\textit {\_Z}}+6 \ln \left ({\mathrm e}^{\textit {\_Z}}-3\right )-6 \ln \relax (2)+6 \ln \relax (5)-6 \textit {\_Z} -15\right )}-2 \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[{y'[x]==-2*x*(y[x]^3-3*y[x]+2),y[1]==-1},y[x],x,IncludeSingularSolutions -> True]
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