12.4.8 problem 8

Internal problem ID [1615]
Book : Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section : Chapter 2, First order equations. Existence and Uniqueness of Solutions of Nonlinear Equations. Section 2.3 Page 60
Problem number : 8
Date solved : Monday, January 27, 2025 at 05:14:01 AM
CAS classification : [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class A`]]

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

✓ Solution by Maple

Time used: 0.110 (sec). Leaf size: 51

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

\[ y = \frac {x \left (\sqrt {7}\, \tan \left (\operatorname {RootOf}\left (\sqrt {7}\, \ln \left (\sec \left (\textit {\_Z} \right )^{2} x^{2}\right )-3 \sqrt {7}\, \ln \left (2\right )+\sqrt {7}\, \ln \left (7\right )+2 \sqrt {7}\, c_1 -4 \textit {\_Z} \right )\right )-1\right )}{4} \]

✓ Solution by Mathematica

Time used: 0.064 (sec). Leaf size: 53

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

\[ \text {Solve}\left [\log \left (\frac {2 y(x)^2}{x^2}+\frac {y(x)}{x}+1\right )-\frac {4 \arctan \left (\frac {\frac {4 y(x)}{x}+1}{\sqrt {7}}\right )}{\sqrt {7}}=-2 \log (x)+c_1,y(x)\right ] \]