Internal problem ID [5038]
Book: Ordinary differential equations and calculus of variations. Makarets and Reshetnyak. Wold
Scientific. Singapore. 1995
Section: Chapter 1. First order differential equations. Section 1.2 Homogeneous equations problems.
page 12
Problem number: 41.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class C], _rational, [_Abel, 2nd type, class A]]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {3 x -y+1}{2 x +y+4}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.957 (sec). Leaf size: 77
dsolve(diff(y(x),x)=(3*x-y(x)+1)/(2*x+y(x)+4),y(x), singsol=all)
\[ -\frac {\ln \left (-\frac {3 \left (x +1\right )^{2}+3 \left (x +1\right ) \left (-y \relax (x )-2\right )-\left (-y \relax (x )-2\right )^{2}}{\left (x +1\right )^{2}}\right )}{2}+\frac {\sqrt {21}\, \arctanh \left (\frac {\left (3 x +7+2 y \relax (x )\right ) \sqrt {21}}{21 x +21}\right )}{21}-\ln \left (x +1\right )-c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.139 (sec). Leaf size: 79
DSolve[y'[x]==(3*x-y[x]+1)/(2*x+y[x]+4),y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [2 \sqrt {21} \tanh ^{-1}\left (\frac {-\frac {10 (x+1)}{y(x)+2 (x+2)}-1}{\sqrt {21}}\right )+21 \left (\log \left (-\frac {-3 x^2+y(x)^2+(3 x+7) y(x)+7}{5 (x+1)^2}\right )+2 \log (x+1)-10 c_1\right )=0,y(x)\right ] \]