Internal problem ID [1052]
Book: Elementary differential equations with boundary value problems. William F. Trench.
Brooks/Cole 2001
Section: Chapter 2, First order equations. Exact equations. Section 2.5 Page 79
Problem number: 23.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _exact, _rational, [_Abel, 2nd type, class A]]
Solve \begin {gather*} \boxed {7 x +4 y+\left (4 x +3 y\right ) y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.037 (sec). Leaf size: 53
dsolve((7*x+4*y(x))+(4*x+3*y(x))*diff(y(x),x)=0,y(x), singsol=all)
\begin{align*} y \relax (x ) = \frac {-\frac {4 x c_{1}}{3}-\frac {\sqrt {-5 c_{1}^{2} x^{2}+3}}{3}}{c_{1}} \\ y \relax (x ) = \frac {-\frac {4 x c_{1}}{3}+\frac {\sqrt {-5 c_{1}^{2} x^{2}+3}}{3}}{c_{1}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.206 (sec). Leaf size: 118
DSolve[(7*x+4*y[x])+(4*x+3*y[x])*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{3} \left (-4 x-\sqrt {-5 x^2+3 e^{2 c_1}}\right ) \\ y(x)\to \frac {1}{3} \left (-4 x+\sqrt {-5 x^2+3 e^{2 c_1}}\right ) \\ y(x)\to \frac {1}{3} \left (-\sqrt {5} \sqrt {-x^2}-4 x\right ) \\ y(x)\to \frac {1}{3} \left (\sqrt {5} \sqrt {-x^2}-4 x\right ) \\ \end{align*}