Internal problem ID [117]
Book: Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section: Section 1.6, Substitution methods and exact equations. Page 74
Problem number: 39.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_exact, _rational]
Solve \begin {gather*} \boxed {3 y^{3} x^{2}+y^{4}+\left (3 y^{2} x^{3}+4 x y^{3}+y^{4}\right ) y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.004 (sec). Leaf size: 29
dsolve(3*x^2*y(x)^3+y(x)^4+(3*x^3*y(x)^2+4*x*y(x)^3+y(x)^4)*diff(y(x),x) = 0,y(x), singsol=all)
\begin{align*} y \relax (x ) = 0 \\ x y \relax (x )^{4}+x^{3} y \relax (x )^{3}+\frac {y \relax (x )^{5}}{5}+c_{1} = 0 \\ \end{align*}
✓ Solution by Mathematica
Time used: 26.335 (sec). Leaf size: 171
DSolve[3*x^2*y[x]^3+y[x]^4+(3*x^3*y[x]^2+4*x*y[x]^3+y[x]^4)*y'[x] == 0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to 0 \\ y(x)\to \text {Root}\left [\text {$\#$1}^5+5 \text {$\#$1}^4 x+5 \text {$\#$1}^3 x^3-5 c_1\&,1\right ] \\ y(x)\to \text {Root}\left [\text {$\#$1}^5+5 \text {$\#$1}^4 x+5 \text {$\#$1}^3 x^3-5 c_1\&,2\right ] \\ y(x)\to \text {Root}\left [\text {$\#$1}^5+5 \text {$\#$1}^4 x+5 \text {$\#$1}^3 x^3-5 c_1\&,3\right ] \\ y(x)\to \text {Root}\left [\text {$\#$1}^5+5 \text {$\#$1}^4 x+5 \text {$\#$1}^3 x^3-5 c_1\&,4\right ] \\ y(x)\to \text {Root}\left [\text {$\#$1}^5+5 \text {$\#$1}^4 x+5 \text {$\#$1}^3 x^3-5 c_1\&,5\right ] \\ y(x)\to 0 \\ \end{align*}