76.4.14 problem 14

Internal problem ID [17408]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 2. First order differential equations. Section 2.6 (Exact equations and integrating factors). Problems at page 100
Problem number : 14
Date solved : Tuesday, January 28, 2025 at 10:06:03 AM
CAS classification : [_exact, _rational, [_1st_order, `_with_symmetry_[F(x),G(x)]`], [_Abel, `2nd type`, `class A`]]

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

With initial conditions

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

✓ Solution by Maple

Time used: 0.049 (sec). Leaf size: 25

dsolve([(9*x^2+y(x)-1) - (4*y(x)-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: 0.150 (sec). Leaf size: 34

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

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