Internal problem ID [1085]
Book: Elementary differential equations with boundary value problems. William F. Trench.
Brooks/Cole 2001
Section: Chapter 2, First order equations. Exact equations. Integrating factors. Section 2.6 Page
91
Problem number: 26.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class G], _rational]
Solve \begin {gather*} \boxed {12 y x +6 y^{3}+\left (9 x^{2}+10 x y^{2}\right ) y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 35
dsolve((12*x*y(x)+6*y(x)^3)+(9*x^2+10*x*y(x)^2)*diff(y(x),x)=0,y(x), singsol=all)
\[ \ln \relax (x )-c_{1}+\frac {6 \ln \left (\frac {y \relax (x )}{\sqrt {x}}\right )}{11}+\frac {2 \ln \left (\frac {2 y \relax (x )^{2}+3 x}{x}\right )}{11} = 0 \]
✓ Solution by Mathematica
Time used: 7.515 (sec). Leaf size: 151
DSolve[(12*x*y[x]+6*y[x]^3)+(9*x^2+10*x*y[x]^2)*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \text {Root}\left [2 \text {$\#$1}^5 x^3+3 \text {$\#$1}^3 x^4-c_1\&,1\right ] \\ y(x)\to \text {Root}\left [2 \text {$\#$1}^5 x^3+3 \text {$\#$1}^3 x^4-c_1\&,2\right ] \\ y(x)\to \text {Root}\left [2 \text {$\#$1}^5 x^3+3 \text {$\#$1}^3 x^4-c_1\&,3\right ] \\ y(x)\to \text {Root}\left [2 \text {$\#$1}^5 x^3+3 \text {$\#$1}^3 x^4-c_1\&,4\right ] \\ y(x)\to \text {Root}\left [2 \text {$\#$1}^5 x^3+3 \text {$\#$1}^3 x^4-c_1\&,5\right ] \\ \end{align*}