83.7.8 problem 5 (b)

Internal problem ID [19126]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter II. Equations of first order and first degree. Exercise II (F) at page 24
Problem number : 5 (b)
Date solved : Tuesday, January 28, 2025 at 12:58:52 PM
CAS classification : [[_homogeneous, `class G`], _rational, [_Abel, `2nd type`, `class B`]]

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

✓ Solution by Maple

Time used: 0.033 (sec). Leaf size: 25

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

\[ y \left (x \right ) = \frac {\operatorname {RootOf}\left (-\ln \left (x \right )+c_{1} +3 \ln \left (\textit {\_Z} \right )+\ln \left (1+2 \textit {\_Z} \right )\right )}{x} \]

✓ Solution by Mathematica

Time used: 60.270 (sec). Leaf size: 1565

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

\begin{align*} y(x)\to \frac {x \sqrt {\frac {1}{x^2}-\frac {64 \sqrt [3]{\frac {2}{3}} e^{c_1}}{\sqrt [3]{\sqrt {3} \sqrt {e^{2 c_1} x^8 \left (27+2048 e^{c_1} x\right )}-9 e^{c_1} x^4}}+\frac {4 \left (\frac {2}{3}\right )^{2/3} \sqrt [3]{\sqrt {3} \sqrt {e^{2 c_1} x^8 \left (27+2048 e^{c_1} x\right )}-9 e^{c_1} x^4}}{x^3}}-4 x \sqrt {\frac {1}{8 x^2}+\frac {4 \sqrt [3]{\frac {2}{3}} e^{c_1}}{\sqrt [3]{\sqrt {3} \sqrt {e^{2 c_1} x^8 \left (27+2048 e^{c_1} x\right )}-9 e^{c_1} x^4}}-\frac {\sqrt [3]{\sqrt {3} \sqrt {e^{2 c_1} x^8 \left (27+2048 e^{c_1} x\right )}-9 e^{c_1} x^4}}{2 \sqrt [3]{2} 3^{2/3} x^3}-\frac {1}{8 x^3 \sqrt {\frac {1}{x^2}-\frac {64 \sqrt [3]{\frac {2}{3}} e^{c_1}}{\sqrt [3]{\sqrt {3} \sqrt {e^{2 c_1} x^8 \left (27+2048 e^{c_1} x\right )}-9 e^{c_1} x^4}}+\frac {4 \left (\frac {2}{3}\right )^{2/3} \sqrt [3]{\sqrt {3} \sqrt {e^{2 c_1} x^8 \left (27+2048 e^{c_1} x\right )}-9 e^{c_1} x^4}}{x^3}}}}-1}{8 x} \\ y(x)\to \frac {x \sqrt {\frac {1}{x^2}-\frac {64 \sqrt [3]{\frac {2}{3}} e^{c_1}}{\sqrt [3]{\sqrt {3} \sqrt {e^{2 c_1} x^8 \left (27+2048 e^{c_1} x\right )}-9 e^{c_1} x^4}}+\frac {4 \left (\frac {2}{3}\right )^{2/3} \sqrt [3]{\sqrt {3} \sqrt {e^{2 c_1} x^8 \left (27+2048 e^{c_1} x\right )}-9 e^{c_1} x^4}}{x^3}}+4 x \sqrt {\frac {1}{8 x^2}+\frac {4 \sqrt [3]{\frac {2}{3}} e^{c_1}}{\sqrt [3]{\sqrt {3} \sqrt {e^{2 c_1} x^8 \left (27+2048 e^{c_1} x\right )}-9 e^{c_1} x^4}}-\frac {\sqrt [3]{\sqrt {3} \sqrt {e^{2 c_1} x^8 \left (27+2048 e^{c_1} x\right )}-9 e^{c_1} x^4}}{2 \sqrt [3]{2} 3^{2/3} x^3}-\frac {1}{8 x^3 \sqrt {\frac {1}{x^2}-\frac {64 \sqrt [3]{\frac {2}{3}} e^{c_1}}{\sqrt [3]{\sqrt {3} \sqrt {e^{2 c_1} x^8 \left (27+2048 e^{c_1} x\right )}-9 e^{c_1} x^4}}+\frac {4 \left (\frac {2}{3}\right )^{2/3} \sqrt [3]{\sqrt {3} \sqrt {e^{2 c_1} x^8 \left (27+2048 e^{c_1} x\right )}-9 e^{c_1} x^4}}{x^3}}}}-1}{8 x} \\ y(x)\to -\frac {x \sqrt {\frac {1}{x^2}-\frac {64 \sqrt [3]{\frac {2}{3}} e^{c_1}}{\sqrt [3]{\sqrt {3} \sqrt {e^{2 c_1} x^8 \left (27+2048 e^{c_1} x\right )}-9 e^{c_1} x^4}}+\frac {4 \left (\frac {2}{3}\right )^{2/3} \sqrt [3]{\sqrt {3} \sqrt {e^{2 c_1} x^8 \left (27+2048 e^{c_1} x\right )}-9 e^{c_1} x^4}}{x^3}}+4 x \sqrt {\frac {1}{8 x^2}+\frac {4 \sqrt [3]{\frac {2}{3}} e^{c_1}}{\sqrt [3]{\sqrt {3} \sqrt {e^{2 c_1} x^8 \left (27+2048 e^{c_1} x\right )}-9 e^{c_1} x^4}}-\frac {\sqrt [3]{\sqrt {3} \sqrt {e^{2 c_1} x^8 \left (27+2048 e^{c_1} x\right )}-9 e^{c_1} x^4}}{2 \sqrt [3]{2} 3^{2/3} x^3}+\frac {1}{8 x^3 \sqrt {\frac {1}{x^2}-\frac {64 \sqrt [3]{\frac {2}{3}} e^{c_1}}{\sqrt [3]{\sqrt {3} \sqrt {e^{2 c_1} x^8 \left (27+2048 e^{c_1} x\right )}-9 e^{c_1} x^4}}+\frac {4 \left (\frac {2}{3}\right )^{2/3} \sqrt [3]{\sqrt {3} \sqrt {e^{2 c_1} x^8 \left (27+2048 e^{c_1} x\right )}-9 e^{c_1} x^4}}{x^3}}}}+1}{8 x} \\ y(x)\to -\frac {x \sqrt {\frac {1}{x^2}-\frac {64 \sqrt [3]{\frac {2}{3}} e^{c_1}}{\sqrt [3]{\sqrt {3} \sqrt {e^{2 c_1} x^8 \left (27+2048 e^{c_1} x\right )}-9 e^{c_1} x^4}}+\frac {4 \left (\frac {2}{3}\right )^{2/3} \sqrt [3]{\sqrt {3} \sqrt {e^{2 c_1} x^8 \left (27+2048 e^{c_1} x\right )}-9 e^{c_1} x^4}}{x^3}}-4 x \sqrt {\frac {1}{8 x^2}+\frac {4 \sqrt [3]{\frac {2}{3}} e^{c_1}}{\sqrt [3]{\sqrt {3} \sqrt {e^{2 c_1} x^8 \left (27+2048 e^{c_1} x\right )}-9 e^{c_1} x^4}}-\frac {\sqrt [3]{\sqrt {3} \sqrt {e^{2 c_1} x^8 \left (27+2048 e^{c_1} x\right )}-9 e^{c_1} x^4}}{2 \sqrt [3]{2} 3^{2/3} x^3}+\frac {1}{8 x^3 \sqrt {\frac {1}{x^2}-\frac {64 \sqrt [3]{\frac {2}{3}} e^{c_1}}{\sqrt [3]{\sqrt {3} \sqrt {e^{2 c_1} x^8 \left (27+2048 e^{c_1} x\right )}-9 e^{c_1} x^4}}+\frac {4 \left (\frac {2}{3}\right )^{2/3} \sqrt [3]{\sqrt {3} \sqrt {e^{2 c_1} x^8 \left (27+2048 e^{c_1} x\right )}-9 e^{c_1} x^4}}{x^3}}}}+1}{8 x} \\ \end{align*}