12.3.17 problem 18

Internal problem ID [1594]
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
Date solved : Monday, January 27, 2025 at 05:12:48 AM
CAS classification : [_separable]

\begin{align*} y^{\prime }&=-2 x \left (y^{3}-3 y+2\right ) \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=3 \end{align*}

✓ Solution by Maple

Time used: 0.325 (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)
 

\[ y = {\mathrm e}^{\operatorname {RootOf}\left (18 x^{2} {\mathrm e}^{\textit {\_Z}}+2 \,{\mathrm e}^{\textit {\_Z}} \ln \left (2\right )-2 \ln \left ({\mathrm e}^{\textit {\_Z}}-3\right ) {\mathrm e}^{\textit {\_Z}}-2 \,{\mathrm e}^{\textit {\_Z}} \ln \left (5\right )+2 \textit {\_Z} \,{\mathrm e}^{\textit {\_Z}}-54 x^{2}+3 \,{\mathrm e}^{\textit {\_Z}}-6 \ln \left (2\right )+6 \ln \left ({\mathrm e}^{\textit {\_Z}}-3\right )+6 \ln \left (5\right )-6 \textit {\_Z} -15\right )}-2 \]

✓ Solution by Mathematica

Time used: 1.070 (sec). Leaf size: 49

DSolve[{D[y[x],x]==-2*x*(y[x]^3-3*y[x]+2),y[0]==3},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \text {InverseFunction}\left [\frac {1}{9} \left (-\frac {3}{\text {$\#$1}-1}-\log (\text {$\#$1}-1)+\log (\text {$\#$1}+2)\right )\&\right ]\left [-x^2-\frac {1}{6}+\frac {1}{9} \log \left (\frac {5}{2}\right )\right ] \]