82.12.7 problem Ex. 7

Internal problem ID [18772]
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. Examples on chapter II at page 29
Problem number : Ex. 7
Date solved : Tuesday, January 28, 2025 at 12:16:37 PM
CAS classification : [_rational, _Bernoulli]

\begin{align*} 3 y^{\prime }+\frac {2 y}{1+x}&=\frac {x^{3}}{y^{2}} \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 135

dsolve(3*diff(y(x),x)+2/(x+1)*y(x)=x^3/y(x)^2,y(x), singsol=all)
 

\begin{align*} y \left (x \right ) &= \frac {450^{{1}/{3}} {\left (\left (10 x^{6}+24 x^{5}+15 x^{4}+60 c_{1} \right ) \left (x +1\right )^{4}\right )}^{{1}/{3}}}{30 \left (x +1\right )^{2}} \\ y \left (x \right ) &= -\frac {450^{{1}/{3}} {\left (\left (10 x^{6}+24 x^{5}+15 x^{4}+60 c_{1} \right ) \left (x +1\right )^{4}\right )}^{{1}/{3}} \left (1+i \sqrt {3}\right )}{60 \left (x +1\right )^{2}} \\ y \left (x \right ) &= \frac {450^{{1}/{3}} {\left (\left (10 x^{6}+24 x^{5}+15 x^{4}+60 c_{1} \right ) \left (x +1\right )^{4}\right )}^{{1}/{3}} \left (i \sqrt {3}-1\right )}{60 \left (x +1\right )^{2}} \\ \end{align*}

✓ Solution by Mathematica

Time used: 4.164 (sec). Leaf size: 144

DSolve[3*D[y[x],x]+2/(x+1)*y[x]==x^3/y[x]^2,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \frac {\sqrt [3]{\frac {10 x^6+24 x^5+15 x^4+60 c_1}{(x+1)^2}}}{2^{2/3} \sqrt [3]{15}} \\ y(x)\to -\frac {\sqrt [3]{-\frac {1}{15}} \sqrt [3]{\frac {10 x^6+24 x^5+15 x^4+60 c_1}{(x+1)^2}}}{2^{2/3}} \\ y(x)\to \frac {(-1)^{2/3} \sqrt [3]{\frac {10 x^6+24 x^5+15 x^4+60 c_1}{(x+1)^2}}}{2^{2/3} \sqrt [3]{15}} \\ \end{align*}