62.8.1 problem Ex 1

Internal problem ID [12829]
Book : An elementary treatise on differential equations by Abraham Cohen. DC heath publishers. 1906
Section : Chapter 2, differential equations of the first order and the first degree. Article 15. Page 22
Problem number : Ex 1
Date solved : Tuesday, January 28, 2025 at 04:25:46 AM
CAS classification : [[_homogeneous, `class G`], _rational, [_Abel, `2nd type`, `class B`]]

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

✓ Solution by Maple

Time used: 3.755 (sec). Leaf size: 39

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

\[ y = \frac {\operatorname {RootOf}\left (x^{2} \textit {\_Z}^{8}-2 \textit {\_Z}^{2} c_{1} -c_{1} \right )^{6} x^{2}-2 c_{1}}{x^{2} c_{1}} \]

✓ Solution by Mathematica

Time used: 0.217 (sec). Leaf size: 68

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

\[ \text {Solve}\left [70^{2/3} \log (x)+54 c_1=54 \int _1^{\frac {4 y(x) x^2+15}{\sqrt [3]{70} \left (2 y(x) x^2+3\right )}}\frac {1}{K[1]^3-\frac {39 K[1]}{70^{2/3}}+1}dK[1],y(x)\right ] \]