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`]]
\[ \boxed {y+\left (x -4 y\right ) y^{\prime }=-9 x^{2}+1} \] With initial conditions \begin {align*} [y \left (1\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.063 (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)
\[ y \left (x \right ) = \frac {x}{4}-\frac {\sqrt {24 x^{3}+x^{2}-8 x -16}}{4} \]
✓ Solution by Mathematica
Time used: 0.148 (sec). Leaf size: 34
DSolve[{-1+9*x^2+y[x]+(x-4*y[x])*y'[x] == 0,y[1]==0},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{4} \left (x+i \sqrt {-24 x^3-x^2+8 x+16}\right ) \]