Internal problem ID [570]
Book: Elementary differential equations and boundary value problems, 10th ed., Boyce and
DiPrima
Section: Miscellaneous problems, end of chapter 2. Page 133
Problem number: 3.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {2 x +y}{3-x +3 y^{2}}=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 75
dsolve([diff(y(x),x) = (2*x+y(x))/(3-x+3*y(x)^2),y(0) = 0],y(x), singsol=all)
\[ y \relax (x ) = \frac {\left (108 x^{2}+12 \sqrt {81 x^{4}-12 x^{3}+108 x^{2}-324 x +324}\right )^{\frac {2}{3}}+12 x -36}{6 \left (108 x^{2}+12 \sqrt {81 x^{4}-12 x^{3}+108 x^{2}-324 x +324}\right )^{\frac {1}{3}}} \]
✓ Solution by Mathematica
Time used: 5.563 (sec). Leaf size: 98
DSolve[{y'[x] == (2*x+y[x])/(3-x+3*y[x]^2),y[0]==0},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {-\sqrt [3]{2} \left (\sqrt {3 x (x (x (27 x-4)+36)-108)+324}-9 x^2\right )^{2/3}-2 \sqrt [3]{3} x+6 \sqrt [3]{3}}{6^{2/3} \sqrt [3]{\sqrt {3 x (x (x (27 x-4)+36)-108)+324}-9 x^2}} \\ \end{align*}