Internal problem ID [11654]
Book: Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi.
2004.
Section: Chapter 2, section 2.3 (Linear equations). Exercises page 56
Problem number: 17.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {y^{\prime }+\left (4 y-\frac {8}{y^{3}}\right ) x=0} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 94
dsolve(diff(y(x),x)+(4*y(x)-8/y(x)^3)*x=0,y(x), singsol=all)
\begin{align*} y \left (x \right ) &= \left (2 \,{\mathrm e}^{8 x^{2}}+c_{1} \right )^{\frac {1}{4}} {\mathrm e}^{-2 x^{2}} \\ y \left (x \right ) &= -\left (2 \,{\mathrm e}^{8 x^{2}}+c_{1} \right )^{\frac {1}{4}} {\mathrm e}^{-2 x^{2}} \\ y \left (x \right ) &= -i \left (2 \,{\mathrm e}^{8 x^{2}}+c_{1} \right )^{\frac {1}{4}} {\mathrm e}^{-2 x^{2}} \\ y \left (x \right ) &= i \left (2 \,{\mathrm e}^{8 x^{2}}+c_{1} \right )^{\frac {1}{4}} {\mathrm e}^{-2 x^{2}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 1.939 (sec). Leaf size: 145
DSolve[y'[x]+(4*y[x]-8/y[x]^3)*x==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\sqrt [4]{2+e^{-8 x^2+4 c_1}} \\ y(x)\to -i \sqrt [4]{2+e^{-8 x^2+4 c_1}} \\ y(x)\to i \sqrt [4]{2+e^{-8 x^2+4 c_1}} \\ y(x)\to \sqrt [4]{2+e^{-8 x^2+4 c_1}} \\ y(x)\to -\sqrt [4]{2} \\ y(x)\to -i \sqrt [4]{2} \\ y(x)\to i \sqrt [4]{2} \\ y(x)\to \sqrt [4]{2} \\ \end{align*}