Internal problem ID [545]
Book: Elementary differential equations and boundary value problems, 10th ed., Boyce and
DiPrima
Section: Section 2.6. Page 100
Problem number: 3.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_exact, _rational]
Solve \begin {gather*} \boxed {2+3 x^{2}-2 y x +\left (3-x^{2}+6 y^{2}\right ) y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.006 (sec). Leaf size: 582
dsolve(2+3*x^2-2*x*y(x)+(3-x^2+6*y(x)^2)*diff(y(x),x) = 0,y(x), singsol=all)
\begin{align*} y \relax (x ) = \frac {\left (-54 x^{3}-54 c_{1}-108 x +6 \sqrt {75 x^{6}+162 c_{1} x^{3}+378 x^{4}+81 c_{1}^{2}+324 x c_{1}+162 x^{2}+162}\right )^{\frac {1}{3}}}{6}-\frac {6 \left (-\frac {x^{2}}{6}+\frac {1}{2}\right )}{\left (-54 x^{3}-54 c_{1}-108 x +6 \sqrt {75 x^{6}+162 c_{1} x^{3}+378 x^{4}+81 c_{1}^{2}+324 x c_{1}+162 x^{2}+162}\right )^{\frac {1}{3}}} \\ y \relax (x ) = -\frac {\left (-54 x^{3}-54 c_{1}-108 x +6 \sqrt {75 x^{6}+162 c_{1} x^{3}+378 x^{4}+81 c_{1}^{2}+324 x c_{1}+162 x^{2}+162}\right )^{\frac {1}{3}}}{12}+\frac {-\frac {x^{2}}{2}+\frac {3}{2}}{\left (-54 x^{3}-54 c_{1}-108 x +6 \sqrt {75 x^{6}+162 c_{1} x^{3}+378 x^{4}+81 c_{1}^{2}+324 x c_{1}+162 x^{2}+162}\right )^{\frac {1}{3}}}-\frac {i \sqrt {3}\, \left (\frac {\left (-54 x^{3}-54 c_{1}-108 x +6 \sqrt {75 x^{6}+162 c_{1} x^{3}+378 x^{4}+81 c_{1}^{2}+324 x c_{1}+162 x^{2}+162}\right )^{\frac {1}{3}}}{6}+\frac {-x^{2}+3}{\left (-54 x^{3}-54 c_{1}-108 x +6 \sqrt {75 x^{6}+162 c_{1} x^{3}+378 x^{4}+81 c_{1}^{2}+324 x c_{1}+162 x^{2}+162}\right )^{\frac {1}{3}}}\right )}{2} \\ y \relax (x ) = -\frac {\left (-54 x^{3}-54 c_{1}-108 x +6 \sqrt {75 x^{6}+162 c_{1} x^{3}+378 x^{4}+81 c_{1}^{2}+324 x c_{1}+162 x^{2}+162}\right )^{\frac {1}{3}}}{12}+\frac {-\frac {x^{2}}{2}+\frac {3}{2}}{\left (-54 x^{3}-54 c_{1}-108 x +6 \sqrt {75 x^{6}+162 c_{1} x^{3}+378 x^{4}+81 c_{1}^{2}+324 x c_{1}+162 x^{2}+162}\right )^{\frac {1}{3}}}+\frac {i \sqrt {3}\, \left (\frac {\left (-54 x^{3}-54 c_{1}-108 x +6 \sqrt {75 x^{6}+162 c_{1} x^{3}+378 x^{4}+81 c_{1}^{2}+324 x c_{1}+162 x^{2}+162}\right )^{\frac {1}{3}}}{6}+\frac {-x^{2}+3}{\left (-54 x^{3}-54 c_{1}-108 x +6 \sqrt {75 x^{6}+162 c_{1} x^{3}+378 x^{4}+81 c_{1}^{2}+324 x c_{1}+162 x^{2}+162}\right )^{\frac {1}{3}}}\right )}{2} \\ \end{align*}
✓ Solution by Mathematica
Time used: 5.017 (sec). Leaf size: 405
DSolve[2+3*x^2-2*x*y[x]+(3-x^2+6*y[x]^2)*y'[x] == 0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {x^2-3}{\sqrt [3]{6} \sqrt [3]{9 x^3+\sqrt {3} \sqrt {-2 \left (x^2-3\right )^3+27 \left (x^3+2 x+c_1\right ){}^2}+18 x+9 c_1}}-\frac {\sqrt [3]{9 x^3+\sqrt {3} \sqrt {-2 \left (x^2-3\right )^3+27 \left (x^3+2 x+c_1\right ){}^2}+18 x+9 c_1}}{6^{2/3}} \\ y(x)\to \frac {2 \sqrt [3]{-6} \left (x^2-3\right )+\left (1-i \sqrt {3}\right ) \left (9 x^3+\sqrt {3} \sqrt {-2 \left (x^2-3\right )^3+27 \left (x^3+2 x+c_1\right ){}^2}+18 x+9 c_1\right ){}^{2/3}}{2\ 6^{2/3} \sqrt [3]{9 x^3+\sqrt {3} \sqrt {-2 \left (x^2-3\right )^3+27 \left (x^3+2 x+c_1\right ){}^2}+18 x+9 c_1}} \\ y(x)\to \frac {\left (x^2-3\right ) \text {Root}\left [\text {$\#$1}^3+48\&,2\right ]+\left (1+i \sqrt {3}\right ) \left (9 x^3+\sqrt {3} \sqrt {-2 \left (x^2-3\right )^3+27 \left (x^3+2 x+c_1\right ){}^2}+18 x+9 c_1\right ){}^{2/3}}{2\ 6^{2/3} \sqrt [3]{9 x^3+\sqrt {3} \sqrt {-2 \left (x^2-3\right )^3+27 \left (x^3+2 x+c_1\right ){}^2}+18 x+9 c_1}} \\ \end{align*}