60.1.234 problem 235

Internal problem ID [10248]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 235
Date solved : Monday, January 27, 2025 at 06:41:36 PM
CAS classification : [[_1st_order, _with_exponential_symmetries], _rational, [_Abel, `2nd type`, `class B`]]

\begin{align*} \left (y x +a \right ) y^{\prime }+b y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.011 (sec). Leaf size: 55

dsolve((x*y(x)+a)*diff(y(x),x)+b*y(x)=0,y(x), singsol=all)
 

\[ \frac {-{\mathrm e}^{\frac {y}{b}} c_{1} b x +\operatorname {Ei}_{1}\left (-\frac {y}{b}\right ) c_{1} a +1}{-{\mathrm e}^{\frac {y}{b}} b x +a \,\operatorname {Ei}_{1}\left (-\frac {y}{b}\right )} = 0 \]

✓ Solution by Mathematica

Time used: 0.084 (sec). Leaf size: 54

DSolve[(x*y[x]+a)*D[y[x],x]+b*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [x=e^{-\frac {y(x)}{b}} \int _1^{y(x)}-\frac {a e^{\frac {K[1]}{b}}}{b K[1]}dK[1]+c_1 e^{-\frac {y(x)}{b}},y(x)\right ] \]