60.1.425 problem 427

Internal problem ID [10439]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 427
Date solved : Monday, January 27, 2025 at 07:43:52 PM
CAS classification : [[_1st_order, _with_linear_symmetries], _rational, _dAlembert]

\begin{align*} \left (3 x +5\right ) {y^{\prime }}^{2}-\left (3 y+x \right ) y^{\prime }+y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.077 (sec). Leaf size: 60

dsolve((3*x+5)*diff(y(x),x)^2-(3*y(x)+x)*diff(y(x),x)+y(x) = 0,y(x), singsol=all)
 

\begin{align*} y &= \frac {x}{3}+\frac {10}{9}-\frac {2 \sqrt {15 x +25}}{9} \\ y &= \frac {x}{3}+\frac {10}{9}+\frac {2 \sqrt {15 x +25}}{9} \\ y &= \frac {\left (3 x +5\right ) c_{1}^{2}-c_{1} x}{3 c_{1} -1} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.018 (sec). Leaf size: 80

DSolve[y[x] - (x + 3*y[x])*D[y[x],x] + (5 + 3*x)*D[y[x],x]^2==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to c_1 \left (x+\frac {5 c_1}{-1+3 c_1}\right ) \\ y(x)\to \frac {1}{9} \left (3 x-2 \sqrt {5} \sqrt {3 x+5}+10\right ) \\ y(x)\to \frac {1}{9} \left (3 x+2 \sqrt {5} \sqrt {3 x+5}+10\right ) \\ \end{align*}