76.4.6 problem 6

Internal problem ID [17400]
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 : 6
Date solved : Tuesday, January 28, 2025 at 10:04:44 AM
CAS classification : [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} y^{\prime }&=-\frac {4 x -2 y}{2 x -3 y} \end{align*}

✓ Solution by Maple

Time used: 20.641 (sec). Leaf size: 52

dsolve(diff(y(x),x)=-(4*x-2*y(x))/(2*x-3*y(x)),y(x), singsol=all)
 

\[ y = \frac {\operatorname {RootOf}\left (-4 c_{1}^{2} x^{2}+3 \textit {\_Z}^{2}-{\mathrm e}^{2 \operatorname {RootOf}\left (3 \,{\mathrm e}^{2 \textit {\_Z}}+12 \operatorname {sech}\left (\sqrt {3}\, \textit {\_Z} \right )^{2} c_{1}^{2} x^{2}\right )}\right )}{c_{1}} \]

✓ Solution by Mathematica

Time used: 0.038 (sec). Leaf size: 40

DSolve[D[y[x],x]==-(4*x-2*y[x])/(2*x-3*y[x]),y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [\int _1^{\frac {y(x)}{x}}\frac {3 K[1]-2}{3 K[1]^2-4}dK[1]=-\log (x)+c_1,y(x)\right ] \]