10.5.14 problem 14

Internal problem ID [1206]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Section 2.6. Page 100
Problem number : 14
Date solved : Monday, January 27, 2025 at 04:45:11 AM
CAS classification : [_exact, _rational, [_1st_order, `_with_symmetry_[F(x),G(x)]`], [_Abel, `2nd type`, `class A`]]

\begin{align*} -1+9 x^{2}+y+\left (x -4 y\right ) y^{\prime }&=0 \end{align*}

With initial conditions

\begin{align*} y \left (1\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.036 (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)
 

\[ y = \frac {x}{4}-\frac {\sqrt {24 x^{3}+x^{2}-8 x -16}}{4} \]

✓ Solution by Mathematica

Time used: 0.138 (sec). Leaf size: 34

DSolve[{-1+9*x^2+y[x]+(x-4*y[x])*D[y[x],x] == 0,y[1]==0},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{4} \left (x+i \sqrt {-24 x^3-x^2+8 x+16}\right ) \]