60.1.424 problem 426

Internal problem ID [10438]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 426
Date solved : Monday, January 27, 2025 at 07:43:51 PM
CAS classification : [[_1st_order, _with_linear_symmetries], _Clairaut]

\begin{align*} \left (1+3 x \right ) {y^{\prime }}^{2}-3 \left (y+2\right ) y^{\prime }+9&=0 \end{align*}

✓ Solution by Maple

Time used: 0.073 (sec). Leaf size: 51

dsolve((3*x+1)*diff(y(x),x)^2-3*(y(x)+2)*diff(y(x),x)+9 = 0,y(x), singsol=all)
 

\begin{align*} y &= -2-2 \sqrt {3 x +1} \\ y &= -2+2 \sqrt {3 x +1} \\ y &= \frac {9+\left (3 x +1\right ) c_{1}^{2}-6 c_{1}}{3 c_{1}} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.015 (sec). Leaf size: 60

DSolve[9 - 3*(2 + y[x])*D[y[x],x] + (1 + 3*x)*D[y[x],x]^2==0,y[x],x,IncludeSingularSolutions -> True]
 

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