82.9.2 problem Ex. 2

Internal problem ID [18754]
Book : Introductory Course On Differential Equations by Daniel A Murray. Longmans Green and Co. NY. 1924
Section : Chapter II. Equations of the first order and of the first degree. Exercises at page 26
Problem number : Ex. 2
Date solved : Tuesday, January 28, 2025 at 12:15:02 PM
CAS classification : [[_homogeneous, `class G`], _rational]

\begin{align*} 2 x^{2} y-3 y^{4}+\left (3 x^{3}+2 x y^{3}\right ) y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.323 (sec). Leaf size: 40

dsolve((2*x^2*y(x)-3*y(x)^4)+(3*x^3+2*x*y(x)^3)*diff(y(x),x)=0,y(x), singsol=all)
 

\[ y \left (x \right ) = {\left (\frac {1}{x \operatorname {RootOf}\left (12 x^{4} \textit {\_Z}^{26}+x^{4} \textit {\_Z}^{16}-5 \,{\mathrm e}^{4 c_{1}}\right )^{13}}\right )}^{{2}/{3}} {\mathrm e}^{\frac {4 c_{1}}{3}} \]

✓ Solution by Mathematica

Time used: 60.220 (sec). Leaf size: 8672

DSolve[(2*x^2*y[x]-3*y[x]^4)+(3*x^3+2*x*y[x]^3)*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

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