Internal problem ID [965]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _rational, [_Abel, 2nd type, class A]]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {2 x +3 y}{x -4 y}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.119 (sec). Leaf size: 46
dsolve(diff(y(x),x)=(2*x+3*y(x))/(x-4*y(x)),y(x), singsol=all)
\[ y \relax (x ) = -\frac {x}{4}+\frac {\sqrt {7}\, x \tan \left (\RootOf \left (\sqrt {7}\, \ln \left (\frac {7 x^{2}}{8}+\frac {7 x^{2} \left (\tan ^{2}\left (\textit {\_Z} \right )\right )}{8}\right )+2 \sqrt {7}\, c_{1}-4 \textit {\_Z} \right )\right )}{4} \]
✓ Solution by Mathematica
Time used: 0.067 (sec). Leaf size: 53
DSolve[y'[x]==(2*x+3*y[x])/(x-4*y[x]),y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\log \left (\frac {2 y(x)^2}{x^2}+\frac {y(x)}{x}+1\right )-\frac {4 \text {ArcTan}\left (\frac {\frac {4 y(x)}{x}+1}{\sqrt {7}}\right )}{\sqrt {7}}=-2 \log (x)+c_1,y(x)\right ] \]