60.1.290 problem 291

Internal problem ID [10304]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 291
Date solved : Monday, January 27, 2025 at 07:05:47 PM
CAS classification : [[_1st_order, _with_linear_symmetries], _rational]

\begin{align*} \left (b \left (\beta y+\alpha x \right )^{2}-\beta \left (a x +b y\right )\right ) y^{\prime }+a \left (\beta y+\alpha x \right )^{2}-\alpha \left (a x +b y\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.041 (sec). Leaf size: 50

dsolve((b*(beta*y(x)+alpha*x)^2-beta*(b*y(x)+a*x))*diff(y(x),x)+a*(beta*y(x)+alpha*x)^2-alpha*(b*y(x)+a*x)=0,y(x), singsol=all)
 

\[ y = \frac {-a x +{\mathrm e}^{\operatorname {RootOf}\left (c_{1} a \beta x -c_{1} \alpha b x -\textit {\_Z} a \beta x +\textit {\_Z} \alpha b x -c_{1} \beta \,{\mathrm e}^{\textit {\_Z}}+{\mathrm e}^{\textit {\_Z}} \textit {\_Z} \beta +b \right )}}{b} \]

✓ Solution by Mathematica

Time used: 0.733 (sec). Leaf size: 39

DSolve[(b*(\[Beta]*y[x]+alpha*x)^2-\[Beta]*(b*y[x]+a*x))*D[y[x],x]+a*(\[Beta]*y[x]+alpha*x)^2-alpha*(b*y[x]+a*x)==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [\frac {a \beta \left (\log (a x+b y(x))+\frac {1}{\alpha x+\beta y(x)}\right )}{a \beta -\alpha b}=c_1,y(x)\right ] \]