60.1.221 problem 222

Internal problem ID [10235]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 222
Date solved : Monday, January 27, 2025 at 06:40:45 PM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} \left (2 y+x +7\right ) y^{\prime }-y+2 x +4&=0 \end{align*}

✓ Solution by Maple

Time used: 0.038 (sec). Leaf size: 32

dsolve((2*y(x)+x+7)*diff(y(x),x)-y(x)+2*x+4=0,y(x), singsol=all)
 

\[ y = -2+\tan \left (\operatorname {RootOf}\left (\ln \left (\sec \left (\textit {\_Z} \right )^{2}\right )-\textit {\_Z} +2 \ln \left (x +3\right )+2 c_{1} \right )\right ) \left (-x -3\right ) \]

✓ Solution by Mathematica

Time used: 0.060 (sec). Leaf size: 65

DSolve[(2*y[x]+x+7)*D[y[x],x]-y[x]+2*x+4==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [2 \arctan \left (\frac {y(x)-2 (x+2)}{2 y(x)+x+7}\right )+2 \log \left (\frac {4 \left (x^2+y(x)^2+4 y(x)+6 x+13\right )}{5 (x+3)^2}\right )+4 \log (x+3)+5 c_1=0,y(x)\right ] \]