20.4.42 problem Problem 60

Internal problem ID [3677]
Book : Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition, 2015
Section : Chapter 1, First-Order Differential Equations. Section 1.8, Change of Variables. page 79
Problem number : Problem 60
Date solved : Monday, January 27, 2025 at 07:54:32 AM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

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

✓ Solution by Maple

Time used: 0.035 (sec). Leaf size: 32

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

\[ y \left (x \right ) = 1+\tan \left (\operatorname {RootOf}\left (4 \textit {\_Z} +\ln \left (\sec \left (\textit {\_Z} \right )^{2}\right )+2 \ln \left (x +1\right )+2 c_{1} \right )\right ) \left (-x -1\right ) \]

✓ Solution by Mathematica

Time used: 0.068 (sec). Leaf size: 68

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

\[ \text {Solve}\left [32 \arctan \left (\frac {-2 y(x)-x+1}{-y(x)+2 x+3}\right )+8 \log \left (\frac {x^2+y(x)^2-2 y(x)+2 x+2}{5 (x+1)^2}\right )+16 \log (x+1)+5 c_1=0,y(x)\right ] \]