47.2.43 problem 41

Internal problem ID [7459]
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
Date solved : Monday, January 27, 2025 at 03:00:56 PM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} y^{\prime }&=\frac {3 x -y+1}{2 x +y+4} \end{align*}

✓ Solution by Maple

Time used: 0.666 (sec). Leaf size: 67

dsolve(diff(y(x),x)=(3*x-y(x)+1)/(2*x+y(x)+4),y(x), singsol=all)
 

\[ -\frac {\ln \left (\frac {y^{2}+\left (3 x +7\right ) y-3 x^{2}+7}{\left (x +1\right )^{2}}\right )}{2}+\frac {\sqrt {21}\, \operatorname {arctanh}\left (\frac {\left (2 y+7+3 x \right ) \sqrt {21}}{21 x +21}\right )}{21}-\ln \left (x +1\right )-c_{1} = 0 \]

✓ Solution by Mathematica

Time used: 0.132 (sec). Leaf size: 79

DSolve[D[y[x],x]==(3*x-y[x]+1)/(2*x+y[x]+4),y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [2 \sqrt {21} \text {arctanh}\left (\frac {-\frac {10 (x+1)}{y(x)+2 (x+2)}-1}{\sqrt {21}}\right )+21 \left (\log \left (-\frac {-3 x^2+y(x)^2+(3 x+7) y(x)+7}{5 (x+1)^2}\right )+2 \log (x+1)-10 c_1\right )=0,y(x)\right ] \]