Internal problem ID [5037]
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`]]
\[ \boxed {y^{\prime }-\frac {3 x -y+1}{2 x +y+4}=0} \]
✓ Solution by Maple
Time used: 0.562 (sec). Leaf size: 77
dsolve(diff(y(x),x)=(3*x-y(x)+1)/(2*x+y(x)+4),y(x), singsol=all)
\[ -\frac {\ln \left (-\frac {3 \left (x +1\right )^{2}+3 \left (x +1\right ) \left (-y \left (x \right )-2\right )-\left (-y \left (x \right )-2\right )^{2}}{\left (x +1\right )^{2}}\right )}{2}+\frac {\sqrt {21}\, \operatorname {arctanh}\left (\frac {\left (2 y \left (x \right )+7+3 x \right ) \sqrt {21}}{21 x +21}\right )}{21}-\ln \left (x +1\right )-c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.132 (sec). Leaf size: 79
DSolve[y'[x]==(3*x-y[x]+1)/(2*x+y[x]+4),y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [2 \sqrt {21} \text {arctanh}\left (\frac {-\frac {10 (x+1)}{y(x)+2 (x+2)}-1}{\sqrt {21}}\right )+21 \left (\log \left (-\frac {-3 x^2+y(x)^2+(3 x+7) y(x)+7}{5 (x+1)^2}\right )+2 \log (x+1)-10 c_1\right )=0,y(x)\right ] \]