Internal problem ID [6025]
Book: Elementary differential equations. By Earl D. Rainville, Phillip E. Bedient. Macmilliam
Publishing Co. NY. 6th edition. 1981.
Section: CHAPTER 16. Nonlinear equations. Section 94. Factoring the left member. EXERCISES
Page 309
Problem number: 12.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [_quadrature]
Solve \begin {gather*} \boxed {\left (4 x -y\right ) \left (y^{\prime }\right )^{2}+6 \left (x -y\right ) y^{\prime }+2 x -5 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 55
dsolve((4*x-y(x))*diff(y(x),x)^2+6*(x-y(x))*diff(y(x),x)+2*x-5*y(x)=0,y(x), singsol=all)
\begin{align*} y \relax (x ) = c_{1}-x \\ y \relax (x ) = -\frac {4 c_{1} x -\sqrt {-12 c_{1} x +1}-1}{2 c_{1}} \\ y \relax (x ) = -\frac {4 c_{1} x +\sqrt {-12 c_{1} x +1}-1}{2 c_{1}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 1.631 (sec). Leaf size: 90
DSolve[(4*x-y[x])*(y'[x])^2+6*(x-y[x])*y'[x]+2*x-5*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{2} \left (-4 x-e^{\frac {c_1}{2}} \sqrt {12 x+e^{c_1}}-e^{c_1}\right ) \\ y(x)\to \frac {1}{2} \left (-4 x+e^{\frac {c_1}{2}} \sqrt {12 x+e^{c_1}}-e^{c_1}\right ) \\ y(x)\to -x+c_1 \\ \end{align*}