Internal problem ID [556]
Book: Elementary differential equations and boundary value problems, 10th ed., Boyce and
DiPrima
Section: Section 2.6. Page 100
Problem number: 14.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_exact, _rational, [_1st_order, _with_symmetry_[F(x),G(x)]], [_Abel, 2nd type, class A]]
Solve \begin {gather*} \boxed {-1+9 x^{2}+y+\left (x -4 y\right ) y^{\prime }=0} \end {gather*} With initial conditions \begin {align*} [y \relax (1) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.044 (sec). Leaf size: 25
dsolve([-1+9*x^2+y(x)+(x-4*y(x))*diff(y(x),x) = 0,y(1) = 0],y(x), singsol=all)
\[ y \relax (x ) = \frac {x}{4}-\frac {\sqrt {24 x^{3}+x^{2}-8 x -16}}{4} \]
✓ Solution by Mathematica
Time used: 0.093 (sec). Leaf size: 32
DSolve[{-1+9*x^2+y[x]+(x-4*y[x])*y'[x] == 0,y[1]==0},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{4} \left (x+i \sqrt {16-x \left (24 x^2+x-8\right )}\right ) \\ \end{align*}