Internal problem ID [1035]
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: 6.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _rational, [_Abel, 2nd type, class A]]
Solve \begin {gather*} \boxed {4 x +7 y+\left (3 x +4 y\right ) y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.217 (sec). Leaf size: 55
dsolve((4*x+7*y(x))+(3*x+4*y(x))*diff(y(x),x)=0,y(x), singsol=all)
\[ y \relax (x ) = -\frac {x \left (2 \RootOf \left (\textit {\_Z}^{36}+3 \textit {\_Z}^{6} c_{1} x^{6}-2 c_{1} x^{6}\right )^{6}-1\right )}{\RootOf \left (\textit {\_Z}^{36}+3 \textit {\_Z}^{6} c_{1} x^{6}-2 c_{1} x^{6}\right )^{6}} \]
✓ Solution by Mathematica
Time used: 1.19 (sec). Leaf size: 409
DSolve[(4*x+7*y[x])+(3*x+4*y[x])*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \text {Root}\left [2 \text {$\#$1}^6+21 \text {$\#$1}^5 x+90 \text {$\#$1}^4 x^2+200 \text {$\#$1}^3 x^3+240 \text {$\#$1}^2 x^4+144 \text {$\#$1} x^5+32 x^6-e^{3 c_1}\&,1\right ] \\ y(x)\to \text {Root}\left [2 \text {$\#$1}^6+21 \text {$\#$1}^5 x+90 \text {$\#$1}^4 x^2+200 \text {$\#$1}^3 x^3+240 \text {$\#$1}^2 x^4+144 \text {$\#$1} x^5+32 x^6-e^{3 c_1}\&,2\right ] \\ y(x)\to \text {Root}\left [2 \text {$\#$1}^6+21 \text {$\#$1}^5 x+90 \text {$\#$1}^4 x^2+200 \text {$\#$1}^3 x^3+240 \text {$\#$1}^2 x^4+144 \text {$\#$1} x^5+32 x^6-e^{3 c_1}\&,3\right ] \\ y(x)\to \text {Root}\left [2 \text {$\#$1}^6+21 \text {$\#$1}^5 x+90 \text {$\#$1}^4 x^2+200 \text {$\#$1}^3 x^3+240 \text {$\#$1}^2 x^4+144 \text {$\#$1} x^5+32 x^6-e^{3 c_1}\&,4\right ] \\ y(x)\to \text {Root}\left [2 \text {$\#$1}^6+21 \text {$\#$1}^5 x+90 \text {$\#$1}^4 x^2+200 \text {$\#$1}^3 x^3+240 \text {$\#$1}^2 x^4+144 \text {$\#$1} x^5+32 x^6-e^{3 c_1}\&,5\right ] \\ y(x)\to \text {Root}\left [2 \text {$\#$1}^6+21 \text {$\#$1}^5 x+90 \text {$\#$1}^4 x^2+200 \text {$\#$1}^3 x^3+240 \text {$\#$1}^2 x^4+144 \text {$\#$1} x^5+32 x^6-e^{3 c_1}\&,6\right ] \\ \end{align*}