60.1.291 problem 292

Internal problem ID [10305]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 292
Date solved : Monday, January 27, 2025 at 07:05:50 PM
CAS classification : [[_homogeneous, `class C`], _rational]

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

✓ Solution by Maple

Time used: 0.015 (sec). Leaf size: 115

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

\[ y = \frac {\left (\left (b x +c \right ) \alpha -\left (\beta x +\gamma \right ) a \right ) \operatorname {RootOf}\left (\int _{}^{\textit {\_Z}}\frac {\left (\textit {\_a} a -b \right )^{2}}{\textit {\_a}^{3} a^{2}-2 \textit {\_a}^{2} a b -\textit {\_a}^{2} \alpha ^{2}+2 \textit {\_a} \alpha \beta +\textit {\_a} \,b^{2}-\beta ^{2}}d \textit {\_a} +\ln \left (a \beta x -\alpha b x +a \gamma -\alpha c \right )+c_{1} \right )+b \gamma -\beta c}{a \beta -b \alpha } \]

✓ Solution by Mathematica

Time used: 3.173 (sec). Leaf size: 2296

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

Too large to display