83.43.4 problem Ex 5 page 7

Internal problem ID [19512]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Book Solved Excercises. Chapter II. Equations of first order and first degree
Problem number : Ex 5 page 7
Date solved : Tuesday, January 28, 2025 at 01:47:15 PM
CAS classification : [[_homogeneous, `class G`], _rational]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 220

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

\begin{align*} y \left (x \right ) &= \frac {\left (108 x +12 \sqrt {12 c_{1}^{3}+81 x^{2}}\right )^{{2}/{3}}-12 c_{1}}{6 \left (108 x +12 \sqrt {12 c_{1}^{3}+81 x^{2}}\right )^{{1}/{3}}} \\ y \left (x \right ) &= -\frac {i \left (108 x +12 \sqrt {12 c_{1}^{3}+81 x^{2}}\right )^{{2}/{3}} \sqrt {3}+12 i c_{1} \sqrt {3}+\left (108 x +12 \sqrt {12 c_{1}^{3}+81 x^{2}}\right )^{{2}/{3}}-12 c_{1}}{12 \left (108 x +12 \sqrt {12 c_{1}^{3}+81 x^{2}}\right )^{{1}/{3}}} \\ y \left (x \right ) &= \frac {i \left (108 x +12 \sqrt {12 c_{1}^{3}+81 x^{2}}\right )^{{2}/{3}} \sqrt {3}+12 i c_{1} \sqrt {3}-\left (108 x +12 \sqrt {12 c_{1}^{3}+81 x^{2}}\right )^{{2}/{3}}+12 c_{1}}{12 \left (108 x +12 \sqrt {12 c_{1}^{3}+81 x^{2}}\right )^{{1}/{3}}} \\ \end{align*}

✓ Solution by Mathematica

Time used: 1.734 (sec). Leaf size: 285

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

\begin{align*} y(x)\to \frac {2 \sqrt [3]{3} c_1-\sqrt [3]{2} \left (-9 x+\sqrt {81 x^2+12 c_1{}^3}\right ){}^{2/3}}{6^{2/3} \sqrt [3]{-9 x+\sqrt {81 x^2+12 c_1{}^3}}} \\ y(x)\to \frac {2^{2/3} \sqrt [3]{3} \left (1-i \sqrt {3}\right ) \left (-9 x+\sqrt {81 x^2+12 c_1{}^3}\right ){}^{2/3}-2 \sqrt [3]{2} \sqrt [6]{3} \left (\sqrt {3}+3 i\right ) c_1}{12 \sqrt [3]{-9 x+\sqrt {81 x^2+12 c_1{}^3}}} \\ y(x)\to \frac {2^{2/3} \sqrt [3]{3} \left (1+i \sqrt {3}\right ) \left (-9 x+\sqrt {81 x^2+12 c_1{}^3}\right ){}^{2/3}-2 \sqrt [3]{2} \sqrt [6]{3} \left (\sqrt {3}-3 i\right ) c_1}{12 \sqrt [3]{-9 x+\sqrt {81 x^2+12 c_1{}^3}}} \\ y(x)\to 0 \\ \end{align*}